Question 1

$\int_{-3}^{0} 2 x \sqrt{25-x^{2}} d x$

Accepted Answer

$\frac{122}{3}$

Question 2

For the problems below, integrate.
-A ball is hurled straight up from the top of a $28 \mathrm{ft}$ building at a velocity of $44 \mathrm{ft} / \mathrm{s}$. a) Find the equation describing the altitude of the ball from the ground. b) How long does it take for the ball to hit the ground? Round to three significant digits.

Accepted Answer

a) $s=-16 t^{2}+44 t+28$
b) 3.28 seconds

Question 3

For the problems below, integrate.
-A capacitor with a capacitance $10^{-3} \mathrm{~F}$ has a voltage of $120 \mathrm{~V}$ across it. At a given instant (t $=0$ ) the capacitor is connected to a source that sends a current $i=6 \sqrt{t}+.01 \mathrm{~A}$ through the circuit. Find the voltage across the capacitor when $\mathrm{t}=0.36 \mathrm{~s}$.

Accepted Answer

$V_{C}=1020 \mathrm{~V}$

Question 4

For the problems below, integrate.
-Find the equation of the curve $y=f(x)$ satisfying the conditions: $\frac{d x}{d y}=\left(x^{2}-6\right)^{3} x d x$ and passing through $(2,5)$.

Accepted Answer

The answer of For the problems below, integrate.
-Find the equation...

Question 5

Integrate $\int\left(6 x^{2}-4 x+9\right) d x$.

Accepted Answer

A)  $12 x-4$ 
B)  $2 x^{3}-2 x^{2}+C$ 
C)  $2 x^{3}-2 x^{2}+9 x+C$ 
D)  $2 x^{3}-x^{4}+9 x+C$ 
A)  $12 x-4$ 
B)  $2 x^{3}-2 x^{2}+C$ 
C)  $2 x^{3}-2 x^{2}+9 x+C$ 
D)  $2 x^{3}-x^{4}+9 x+C$

Question 6

Evaluate the definite integral $\int_{-2}^{0}\left(2 x^{3}-4 x\right) d x$.

Accepted Answer

A)  0 
B)  -2 
C)  4 
D)  2 
A)  0 
B)  -2 
C)  4 
D)  2

Question 7

Recall that the voltage across a capacitor is given by $V_{C}=\frac{1}{C} \int i(t) d t$. Find the formula for $V_{C}$ if $C=$ .01 farad, $i(t)=2 t+3$ amperes, and $V_{C}(0)=12$ volts.

Accepted Answer

A)  $V_{C}(t)=100 t^{2}+300 t^{2}+1200$ volts 
B)  $V_{C}(t)=t^{2}+3 t+1200$ volts 
C)  $V_{C}(t)=100 t^{2}+300 t+12$ volts 
D)  $V_{C}(t)=t^{2}+3 t+12$ volts 
A)  $V_{C}(t)=100 t^{2}+300 t^{2}+1200$ volts 
B)  $V_{C}(t)=t^{2}+3 t+1200$ volts 
C)  $V_{C}(t)=100 t^{2}+300 t+12$ volts 
D)  $V_{C}(t)=t^{2}+3 t+12$ volts

Question 8

Integrate $\int \frac{1}{(5 x+2)^{2}} d x$.

Accepted Answer

A)  $\ln (5 x+2)^{2}+C$ 
B)  $\frac{-1}{5(5 x+2)}+C$ 
C)  $\frac{-1}{5 x+2}+C$ 
D)  $\frac{1}{5} \ln (5 x+2)^{2}+C$ 
A)  $\ln (5 x+2)^{2}+C$ 
B)  $\frac{-1}{5(5 x+2)}+C$ 
C)  $\frac{-1}{5 x+2}+C$ 
D)  $\frac{1}{5} \ln (5 x+2)^{2}+C$

Question 9

Integrate $\int \frac{2 x}{\sqrt{x^{2}+3}} d x$.

Accepted Answer

A)  $\frac{1}{2} \sqrt{\mathrm{x}^{2}+3}+\mathrm{C}$ 
B)  $2 \sqrt{x^{2}+3}+C$ 
C)  $\sqrt{x^{2}+3}+C$ 
D)  $\frac{4}{3}\left(x^{2}+3\right)^{3 / 2}+C$ 
A)  $\frac{1}{2} \sqrt{\mathrm{x}^{2}+3}+\mathrm{C}$ 
B)  $2 \sqrt{x^{2}+3}+C$ 
C)  $\sqrt{x^{2}+3}+C$ 
D)  $\frac{4}{3}\left(x^{2}+3\right)^{3 / 2}+C$

Question 10

$\int_{0}^{4} \frac{18 x}{\sqrt{9 x^{2}+25}} d x$

Accepted Answer

The answer of   \(\int_{0}^{4} \frac{18 x}{\sqrt{9 x^{2}+25}} d...

Question 11

Find the area under the curve $y=4-3 x^{2}$ from $x=0$ to $x=1$.

Accepted Answer

A)  10 
B)  4 
C)  3 
D)  7 
A)  10 
B)  4 
C)  3 
D)  7

Question 12

For the problems below, find the area under the curve.
-  $y=-x^{2}+3 x+10$ from $x=1$ to $x=4$

Accepted Answer

The answer of For the problems below, find the area...

Question 13

For the problems below, find the area under the curve.
-  $y=\sqrt{4 x+1}$ from $x=2$ to $x=6$

Accepted Answer

The answer of For the problems below, find the area...

Question 14

For the problems below, find the area under the curve.
-Find the area bounded by the $x$ - axis and $y=-x^{2}+10 x-16$.

Accepted Answer

The answer of For the problems below, find the area...

Question 15

$\int_{2}^{5}\left(x^{3}-9 x^{2}+6 x-3\right) d x$

Accepted Answer

The answer of   $\int_{2}^{5}\left(x^{3}-9 x^{2}+6 x-3\right) d x$...

Question 16

For the problems below, integrate.
-10 $\int \frac{x^{2} d x}{\left(4 x^{3}-5\right)^{3}}$

Accepted Answer

The answer of For the problems below, integrate.
-10 \(\int \frac{x^{2}...

Question 17

For the problems below, integrate.
-8 $\int 3 x^{23} d x$

Accepted Answer

The answer of For the problems below, integrate.
-8 \(\int 3...

Question 18

For the problems below, evaluate each definite integral.
- $\int_{2}^{3}\left(6 x^{2}-x-6\right) d x$

Accepted Answer

The answer of For the problems below, evaluate each definite...

Question 19

Evaluate the definite integral $\int_{0}^{1}(2 x+1)^{3} d x$.

Accepted Answer

A)  20 
B)  10 
C)  $\frac{81}{4}=20.25$ 
D)  40 
A)  20 
B)  10 
C)  $\frac{81}{4}=20.25$ 
D)  40

Question 20

For the problems below, integrate.
-11 $\int \frac{\left(x^{4}+2 x^{2}\right) d x}{\sqrt[4]{3 x^{5}+10 x^{3}}}$

Accepted Answer

The answer of For the problems below, integrate.
-11 \(\int \frac{\left(x^{4}+2...

$\int_{-3}^{0} 2 x \sqrt{25-x^{2}} d x$

For the problems below, integrate. -Find the equation of the curve $y=f(x)$ satisfying the conditions: $\frac{d x}{d y}=\left(x^{2}-6\right)^{3} x d x$ and passing through $(2,5)$ .

Integrate $\int\left(6 x^{2}-4 x+9\right) d x$ .

Evaluate the definite integral $\int_{-2}^{0}\left(2 x^{3}-4 x\right) d x$ .

Recall that the voltage across a capacitor is given by $V_{C}=\frac{1}{C} \int i(t) d t$ . Find the formula for $V_{C}$ if $C=$ .01 farad, $i(t)=2 t+3$ amperes, and $V_{C}(0)=12$ volts.

Integrate $\int \frac{1}{(5 x+2)^{2}} d x$ .

Integrate $\int \frac{2 x}{\sqrt{x^{2}+3}} d x$ .

$\int_{0}^{4} \frac{18 x}{\sqrt{9 x^{2}+25}} d x$

Find the area under the curve $y=4-3 x^{2}$ from $x=0$ to $x=1$ .

For the problems below, find the area under the curve. - $y=-x^{2}+3 x+10$ from $x=1$ to $x=4$

For the problems below, find the area under the curve. - $y=\sqrt{4 x+1}$ from $x=2$ to $x=6$

For the problems below, find the area under the curve. -Find the area bounded by the $x$ - axis and $y=-x^{2}+10 x-16$ .

$\int_{2}^{5}\left(x^{3}-9 x^{2}+6 x-3\right) d x$

For the problems below, integrate. -10 $\int \frac{x^{2} d x}{\left(4 x^{3}-5\right)^{3}}$

For the problems below, integrate. -8 $\int 3 x^{23} d x$

For the problems below, evaluate each definite integral. - $\int_{2}^{3}\left(6 x^{2}-x-6\right) d x$

Evaluate the definite integral $\int_{0}^{1}(2 x+1)^{3} d x$ .

For the problems below, integrate. -11 $\int \frac{\left(x^{4}+2 x^{2}\right) d x}{\sqrt[4]{3 x^{5}+10 x^{3}}}$

Analytic Geometry

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

Exam 5: The Integral

∫−302x25−x2dx\int_{-3}^{0} 2 x \sqrt{25-x^{2}} d x∫−30​2x25−x2​dx

For the problems below, integrate. -Find the equation of the curve y=f(x)y=f(x)y=f(x) satisfying the conditions: dxdy=(x2−6)3xdx\frac{d x}{d y}=\left(x^{2}-6\right)^{3} x d xdydx​=(x2−6)3xdx and passing through (2,5)(2,5)(2,5) .

Integrate ∫(6x2−4x+9)dx\int\left(6 x^{2}-4 x+9\right) d x∫(6x2−4x+9)dx .

Evaluate the definite integral ∫−20(2x3−4x)dx\int_{-2}^{0}\left(2 x^{3}-4 x\right) d x∫−20​(2x3−4x)dx .

Recall that the voltage across a capacitor is given by VC=1C∫i(t)dtV_{C}=\frac{1}{C} \int i(t) d tVC​=C1​∫i(t)dt . Find the formula for VCV_{C}VC​ if C=C=C= .01 farad, i(t)=2t+3i(t)=2 t+3i(t)=2t+3 amperes, and VC(0)=12V_{C}(0)=12VC​(0)=12 volts.

Integrate ∫1(5x+2)2dx\int \frac{1}{(5 x+2)^{2}} d x∫(5x+2)21​dx .

Integrate ∫2xx2+3dx\int \frac{2 x}{\sqrt{x^{2}+3}} d x∫x2+3​2x​dx .

∫0418x9x2+25dx\int_{0}^{4} \frac{18 x}{\sqrt{9 x^{2}+25}} d x∫04​9x2+25​18x​dx

Find the area under the curve y=4−3x2y=4-3 x^{2}y=4−3x2 from x=0x=0x=0 to x=1x=1x=1 .

For the problems below, find the area under the curve. - y=−x2+3x+10y=-x^{2}+3 x+10y=−x2+3x+10 from x=1x=1x=1 to x=4x=4x=4

For the problems below, find the area under the curve. - y=4x+1y=\sqrt{4 x+1}y=4x+1​ from x=2x=2x=2 to x=6x=6x=6

For the problems below, find the area under the curve. -Find the area bounded by the xxx - axis and y=−x2+10x−16y=-x^{2}+10 x-16y=−x2+10x−16 .

∫25(x3−9x2+6x−3)dx\int_{2}^{5}\left(x^{3}-9 x^{2}+6 x-3\right) d x∫25​(x3−9x2+6x−3)dx

For the problems below, integrate. -10 ∫x2dx(4x3−5)3\int \frac{x^{2} d x}{\left(4 x^{3}-5\right)^{3}}∫(4x3−5)3x2dx​

For the problems below, integrate. -8 ∫3x23dx\int 3 x^{23} d x∫3x23dx

For the problems below, evaluate each definite integral. - ∫23(6x2−x−6)dx\int_{2}^{3}\left(6 x^{2}-x-6\right) d x∫23​(6x2−x−6)dx

Evaluate the definite integral ∫01(2x+1)3dx\int_{0}^{1}(2 x+1)^{3} d x∫01​(2x+1)3dx .

For the problems below, integrate. -11 ∫(x4+2x2)dx3x5+10x34\int \frac{\left(x^{4}+2 x^{2}\right) d x}{\sqrt[4]{3 x^{5}+10 x^{3}}}∫43x5+10x3​(x4+2x2)dx​

Analytic Geometry

The Derivative

Applications of the Derivative

Derivatives of Transcendental Functions

Applications of Integration

Methods of Integration

Three-Space: Partial Derivatives and Double Integrals

Progressions and the Binomial Theorem

Series

First-Order Differential Equations

Second-Order Differential Equations

Filters

$\int_{-3}^{0} 2 x \sqrt{25-x^{2}} d x$

For the problems below, integrate. -Find the equation of the curve $y=f(x)$ satisfying the conditions: $\frac{d x}{d y}=\left(x^{2}-6\right)^{3} x d x$ and passing through $(2,5)$ .

Integrate $\int\left(6 x^{2}-4 x+9\right) d x$ .

Evaluate the definite integral $\int_{-2}^{0}\left(2 x^{3}-4 x\right) d x$ .

Recall that the voltage across a capacitor is given by $V_{C}=\frac{1}{C} \int i(t) d t$ . Find the formula for $V_{C}$ if $C=$ .01 farad, $i(t)=2 t+3$ amperes, and $V_{C}(0)=12$ volts.

Integrate $\int \frac{1}{(5 x+2)^{2}} d x$ .

Integrate $\int \frac{2 x}{\sqrt{x^{2}+3}} d x$ .

$\int_{0}^{4} \frac{18 x}{\sqrt{9 x^{2}+25}} d x$

Find the area under the curve $y=4-3 x^{2}$ from $x=0$ to $x=1$ .

For the problems below, find the area under the curve. - $y=-x^{2}+3 x+10$ from $x=1$ to $x=4$

For the problems below, find the area under the curve. - $y=\sqrt{4 x+1}$ from $x=2$ to $x=6$

For the problems below, find the area under the curve. -Find the area bounded by the $x$ - axis and $y=-x^{2}+10 x-16$ .

$\int_{2}^{5}\left(x^{3}-9 x^{2}+6 x-3\right) d x$

For the problems below, integrate. -10 $\int \frac{x^{2} d x}{\left(4 x^{3}-5\right)^{3}}$

For the problems below, integrate. -8 $\int 3 x^{23} d x$

For the problems below, evaluate each definite integral. - $\int_{2}^{3}\left(6 x^{2}-x-6\right) d x$

Evaluate the definite integral $\int_{0}^{1}(2 x+1)^{3} d x$ .

For the problems below, integrate. -11 $\int \frac{\left(x^{4}+2 x^{2}\right) d x}{\sqrt[4]{3 x^{5}+10 x^{3}}}$