Question 1

Find the exact area between the graphs of $y=x^{3}+9$ and $y=-x+9$ for 0$\le$ x $\le$ 5.

Accepted Answer

The answer of Find the exact area between the graphs...

Question 2

A car is going 64 feet per second and the driver puts on the brakes, bringing the car to a stop in 4 seconds.Assume the deceleration of the car is constant while the brakes are on.The acceleration (really deceleration)of the car is _____ ft/sec.

Accepted Answer

The answer of A car is going 64 feet per...

Question 3

A young girl who aspires to be a rocket scientist launches a model rocket from the ground at time t = 0.The rocket travels straight up in the air, and the following graph shows the upward velocity of the rocket as a function of time:   Let v(t)be the function that gives the velocity of the rocket at time t.From the graph of the rocket's velocity, which of the following is larger?

Accepted Answer

A)  $\left|\int_{0}^{t_{2}} v(t) d t\right|$ 
B)  $\left|\int_{t_{2}}^{t_{3}} v(t) d t\right|$ 
A)  $\left|\int_{0}^{t_{2}} v(t) d t\right|$ 
B)  $\left|\int_{t_{2}}^{t_{3}} v(t) d t\right|$

Question 4

Find the total area bounded between the curve $f(x)=x^{3}-3 x^{2}+2 x$ and the x-axis.Round to 3 decimal places.

Accepted Answer

The answer of Find the total area bounded between the...

Question 5

The general antiderivative for $g(x)=7 \sin 3 x-8 \cos 9 x$ is given by $-21 \cos 3 x-72 \sin 9 x+C$ .

Accepted Answer

A) True 
 B)False

Question 6

You decide to take a trip down a stretch of road that runs straight east and west.The following table gives your eastward velocity (in miles per minute)measured at one-minute intervals for the first ten minutes of your trip. $\begin{array}{cccccccccccc}
\text { Time (min) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\text { Velocity } & 0.00 & 0.49 & 0.84 & 1.05 & 1.12 & 1.05 & 0.84 & 0.49 & 0.00 & -0.63 & -1.4
\
\text { (mi/min)}
\end{array}$  Does the following graph give your acceleration or your eastward distance from your starting place as a function of time?

Accepted Answer

A) Your acceleration 
B) Your eastward distance 
A) Your acceleration 
B) Your eastward distance

Question 7

Evaluate $\frac{d}{d x} \int_{1}^{x^{3}} \sin t d t$ .

Accepted Answer

The answer of Evaluate \(\frac{d}{d x} \int_{1}^{x^{3}} \sin t d...

Question 8

Suppose $F(x)=5 \sin x+x+7$ .Find the total area bounded by F(x), x = 0, x =  $\pi$ and y = 0.Round to 2 decimal places.

Accepted Answer

The answer of Suppose $F(x)=5 \sin x+x+7$ .Find the total...

Question 9

A car is going 56 feet per second and the driver puts on the brakes, bringing the car to a stop in 4 seconds.Assume the deceleration of the car is constant while the brakes are on.How many feet does the car travel from the time the brakes are applied until it stops?

Accepted Answer

The answer of A car is going 56 feet per...

Question 10

The graph of $g(t)$ is shown in the following figure.If G is an antiderivative of g such that $G(0)=-6$ , what is $G(5)$ ?

Accepted Answer

The answer of The graph of $g(t)$ is shown in...

Question 11

Determine: $\int \frac{x^{2}-2 x^{7}}{x^{3}} d x$

Accepted Answer

The answer of Determine: $\int \frac{x^{2}-2 x^{7}}{x^{3}} d x$...

Question 12

For $-4 \leq x \leq 4$ , define $F(x)=\int_{-4}^{x} \sqrt{16-t^{2}} d t$ .Find F'(x).

Accepted Answer

A)  $\sqrt{2 x}$ 
B)  $-\sqrt{2 x}$ 
C)  $-\sqrt{16-x^{2}}$ 
D)  $\sqrt{16-x^{2}}$ 
A)  $\sqrt{2 x}$ 
B)  $-\sqrt{2 x}$ 
C)  $-\sqrt{16-x^{2}}$ 
D)  $\sqrt{16-x^{2}}$

Question 13

A young girl who aspires to be a rocket scientist launches a model rocket from the ground at time t = 0.The rocket travels straight up in the air, and the following graph shows the upward velocity of the rocket as a function of time:   Let h be the height (or vertical displacement)of the rocket, let a be the acceleration of the rocket, and let h = 0 be the ground level from which the rocket was launched.Recall that the first derivative of displacement is velocity and that the first derivative of velocity is acceleration.Is the following a graph of the acceleration or the height of the rocket as a function of time?

Accepted Answer

A) The acceleration. 
B) The height. 
A) The acceleration. 
B) The height.

Question 14

A boulder is dropped from a 150-foot cliff.How fast is it going when it hits the ground? Round to 2 decimal places.

Accepted Answer

The answer of A boulder is dropped from a 150-foot...

Question 15

For $H(x)=\int_{0}^{x} 6 t^{2} d t$ , find $H(1)$ .

Accepted Answer

The answer of For $H(x)=\int_{0}^{x} 6 t^{2} d t$ ,...

Question 16

Sketch the graphs of $y=e^{x}$ and y = ex.Find the average value of the difference between $e^{x}$ and ex on the interval between x = 0 and x = 1.5.Round to 2 decimal places.

Accepted Answer

The answer of Sketch the graphs of $y=e^{x}$ and y...

Question 17

The figure shown represents the velocity of a particle over time.
True or False: The area under the curve represents the particle traveling south.

Accepted Answer

A) True 
 B)False

Question 18

Find the area of the region between $y_{1}=-2(x-4)^{2}+32$ and $y_{2}=x$ , accurate to 2 decimal places.

Accepted Answer

The answer of Find the area of the region between...

Question 19

The police observe that the skid marks made by a stopping car are 240 ft long.Assuming the car decelerated at a constant rate of 21 ft/ sec2, skidding all the way, how fast was the car going when the brakes were applied? Round to 2 decimal places.

Accepted Answer

Question 20

If the graph below is of $f(x)$ where $F^{\prime}(x)=f(x)$ , which of the equations below could represent $F(x)$ ?

Accepted Answer

A) 2 
B) 2x 
C)  $2 x+3$ 
D)  $x^{2}+3$ 
E) None of the above. 
A) 2 
B) 2x 
C)  $2 x+3$ 
D)  $x^{2}+3$ 
E) None of the above.

Find the exact area between the graphs of $y=x^{3}+9$ and $y=-x+9$ for 0 $\le$ x $\le$ 5.

A car is going 64 feet per second and the driver puts on the brakes, bringing the car to a stop in 4 seconds.Assume the deceleration of the car is constant while the brakes are on.The acceleration (really deceleration)of the car is _____ ft/sec.

Find the total area bounded between the curve $f(x)=x^{3}-3 x^{2}+2 x$ and the x-axis.Round to 3 decimal places.

The general antiderivative for $g(x)=7 \sin 3 x-8 \cos 9 x$ is given by $-21 \cos 3 x-72 \sin 9 x+C$ .

Evaluate $\frac{d}{d x} \int_{1}^{x^{3}} \sin t d t$ .

Suppose $F(x)=5 \sin x+x+7$ .Find the total area bounded by F(x), x = 0, x = $\pi$ and y = 0.Round to 2 decimal places.

A car is going 56 feet per second and the driver puts on the brakes, bringing the car to a stop in 4 seconds.Assume the deceleration of the car is constant while the brakes are on.How many feet does the car travel from the time the brakes are applied until it stops?

The graph of $g(t)$ is shown in the following figure.If G is an antiderivative of g such that $G(0)=-6$ , what is $G(5)$ ?

Determine: $\int \frac{x^{2}-2 x^{7}}{x^{3}} d x$

For $-4 \leq x \leq 4$ , define $F(x)=\int_{-4}^{x} \sqrt{16-t^{2}} d t$ .Find F'(x).

A boulder is dropped from a 150-foot cliff.How fast is it going when it hits the ground? Round to 2 decimal places.

For $H(x)=\int_{0}^{x} 6 t^{2} d t$ , find $H(1)$ .

Sketch the graphs of $y=e^{x}$ and y = ex.Find the average value of the difference between $e^{x}$ and ex on the interval between x = 0 and x = 1.5.Round to 2 decimal places.

The figure shown represents the velocity of a particle over time. True or False: The area under the curve represents the particle traveling south.

Find the area of the region between $y_{1}=-2(x-4)^{2}+32$ and $y_{2}=x$ , accurate to 2 decimal places.

The police observe that the skid marks made by a stopping car are 240 ft long.Assuming the car decelerated at a constant rate of 21 ft/ sec², skidding all the way, how fast was the car going when the brakes were applied? Round to 2 decimal places.

If the graph below is of $f(x)$ where $F^{\prime}(x)=f(x)$ , which of the equations below could represent $F(x)$ ? $If the graph below is of f(x) where F^{\prime}(x)=f(x) , which of the equations below could represent F(x) ?$

A Library of Functions

Key Concept: the Derivative

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Exam 6: Constructing Antiderivatives

Find the exact area between the graphs of y=x3+9y=x^{3}+9y=x3+9 and y=−x+9y=-x+9y=−x+9 for 0 ≤\le≤ x ≤\le≤ 5.

A car is going 64 feet per second and the driver puts on the brakes, bringing the car to a stop in 4 seconds.Assume the deceleration of the car is constant while the brakes are on.The acceleration (really deceleration)of the car is _____ ft/sec.

Find the total area bounded between the curve f(x)=x3−3x2+2xf(x)=x^{3}-3 x^{2}+2 xf(x)=x3−3x2+2x and the x-axis.Round to 3 decimal places.

The general antiderivative for g(x)=7sin⁡3x−8cos⁡9xg(x)=7 \sin 3 x-8 \cos 9 xg(x)=7sin3x−8cos9x is given by −21cos⁡3x−72sin⁡9x+C-21 \cos 3 x-72 \sin 9 x+C−21cos3x−72sin9x+C .

Evaluate ddx∫1x3sin⁡tdt\frac{d}{d x} \int_{1}^{x^{3}} \sin t d tdxd​∫1x3​sintdt .

Suppose F(x)=5sin⁡x+x+7F(x)=5 \sin x+x+7F(x)=5sinx+x+7 .Find the total area bounded by F(x), x = 0, x = π\piπ and y = 0.Round to 2 decimal places.

A car is going 56 feet per second and the driver puts on the brakes, bringing the car to a stop in 4 seconds.Assume the deceleration of the car is constant while the brakes are on.How many feet does the car travel from the time the brakes are applied until it stops?

The graph of g(t)g(t)g(t) is shown in the following figure.If G is an antiderivative of g such that G(0)=−6G(0)=-6G(0)=−6 , what is G(5)G(5)G(5) ?

Determine: ∫x2−2x7x3dx\int \frac{x^{2}-2 x^{7}}{x^{3}} d x∫x3x2−2x7​dx

For −4≤x≤4-4 \leq x \leq 4−4≤x≤4 , define F(x)=∫−4x16−t2dtF(x)=\int_{-4}^{x} \sqrt{16-t^{2}} d tF(x)=∫−4x​16−t2​dt .Find F'(x).

A boulder is dropped from a 150-foot cliff.How fast is it going when it hits the ground? Round to 2 decimal places.

For H(x)=∫0x6t2dtH(x)=\int_{0}^{x} 6 t^{2} d tH(x)=∫0x​6t2dt , find H(1)H(1)H(1) .

Sketch the graphs of y=exy=e^{x}y=ex and y = ex.Find the average value of the difference between exe^{x}ex and ex on the interval between x = 0 and x = 1.5.Round to 2 decimal places.

The figure shown represents the velocity of a particle over time. True or False: The area under the curve represents the particle traveling south.

Find the area of the region between y1=−2(x−4)2+32y_{1}=-2(x-4)^{2}+32y1​=−2(x−4)2+32 and y2=xy_{2}=xy2​=x , accurate to 2 decimal places.

The police observe that the skid marks made by a stopping car are 240 ft long.Assuming the car decelerated at a constant rate of 21 ft/ sec2, skidding all the way, how fast was the car going when the brakes were applied? Round to 2 decimal places.

If the graph below is of f(x)f(x)f(x) where F′(x)=f(x)F^{\prime}(x)=f(x)F′(x)=f(x) , which of the equations below could represent F(x)F(x)F(x) ?

A Library of Functions

Key Concept: the Derivative

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Find the exact area between the graphs of $y=x^{3}+9$ and $y=-x+9$ for 0 $\le$ x $\le$ 5.

Find the total area bounded between the curve $f(x)=x^{3}-3 x^{2}+2 x$ and the x-axis.Round to 3 decimal places.

The general antiderivative for $g(x)=7 \sin 3 x-8 \cos 9 x$ is given by $-21 \cos 3 x-72 \sin 9 x+C$ .

Evaluate $\frac{d}{d x} \int_{1}^{x^{3}} \sin t d t$ .

Suppose $F(x)=5 \sin x+x+7$ .Find the total area bounded by F(x), x = 0, x = $\pi$ and y = 0.Round to 2 decimal places.

The graph of $g(t)$ is shown in the following figure.If G is an antiderivative of g such that $G(0)=-6$ , what is $G(5)$ ?

Determine: $\int \frac{x^{2}-2 x^{7}}{x^{3}} d x$

For $-4 \leq x \leq 4$ , define $F(x)=\int_{-4}^{x} \sqrt{16-t^{2}} d t$ .Find F'(x).

For $H(x)=\int_{0}^{x} 6 t^{2} d t$ , find $H(1)$ .

Sketch the graphs of $y=e^{x}$ and y = ex.Find the average value of the difference between $e^{x}$ and ex on the interval between x = 0 and x = 1.5.Round to 2 decimal places.

Find the area of the region between $y_{1}=-2(x-4)^{2}+32$ and $y_{2}=x$ , accurate to 2 decimal places.

The police observe that the skid marks made by a stopping car are 240 ft long.Assuming the car decelerated at a constant rate of 21 ft/ sec², skidding all the way, how fast was the car going when the brakes were applied? Round to 2 decimal places.

If the graph below is of $f(x)$ where $F^{\prime}(x)=f(x)$ , which of the equations below could represent $F(x)$ ? $If the graph below is of f(x) where F^{\prime}(x)=f(x) , which of the equations below could represent F(x) ?$