Question 1

Find the values of c such that the area of the region bounded by the parabolas   is   .

Accepted Answer

The answer of Find the values of c such that...

Question 2

Use a graphing utility to (a) plot the graphs of the given functions and (b) find the approximate x-coordinates of the points of intersection of the graphs. Then find an approximation of the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the x-axis. Round answers to two decimal places.
y =   x5, y = 3x2 - x3

Accepted Answer

a. @#IMG-DLM&
b. (0,

Question 3

Sketch the region bounded by the graphs of the given equations and find the area of their region. x = y2 + 2, x = y - 2, y = -3, y = 3

Accepted Answer

A)      
B)      
C)      
D)      
A)      
B)      
C)      
D)

Question 4

Find the area of the region bounded by the given curves.

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 5

Find the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Evaluate the integral using an appropriate trigonometric substitution.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Find the area of the region bounded by the curves.

Accepted Answer

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

Question 8

Find the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Evaluate the integral.

Accepted Answer

A) 14 
B) 10 
C) -11 
D) -14 
A) 14 
B) 10 
C) -11 
D) -14

Question 10

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

The base of a solid is a circular disk with radius   . Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

Accepted Answer

A) 7 
B) 16 
C) 49 
D) 6 
E) None of these 
A) 7 
B) 16 
C) 49 
D) 6 
E) None of these

Question 12

The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b].

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Use integration to find the area of the triangle with the given vertices. (0, 0), (1, 9), (4, 2)

Accepted Answer

A)    
B)    
C) 36 
D) 34 
A)    
B)    
C) 36 
D) 34

Question 14

Evaluate the limit by interpreting it as the limit of a Riemann sum of a function on the interval [a, b].

Accepted Answer

A)    
B) -   
C) -   
D)    
A)    
B) -   
C) -   
D)

Question 15

Find the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

Sketch the region bounded by the graphs of the given equations and find the area of that region.
y = -x2 + 4, y = 6x + 5

Accepted Answer

Question 17

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle. y = 25 - x2, y = 0; the line

Accepted Answer

A)    $\pi$
  
B)    $\pi$
  
C)    $\pi$
  
D)    $\pi$
  
A)    $\pi$
  
B)    $\pi$
  
C)    $\pi$
  
D)    $\pi$

Question 18

Find the volume of the frustum of a pyramid with square base of side   square top of side   and height

Accepted Answer

The answer of Find the volume of the frustum of...

Question 19

Find the indefinite integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 20

Find the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Find the values of c such that the area of the region bounded by the parabolas is .

Sketch the region bounded by the graphs of the given equations and find the area of their region. x = y² + 2, x = y - 2, y = -3, y = 3

Find the area of the region bounded by the given curves.

Find the integral.

Evaluate the integral using an appropriate trigonometric substitution.

Find the area of the region bounded by the curves.

Find the integral.

Evaluate the integral.

Find the integral using an appropriate trigonometric substitution.

The base of a solid is a circular disk with radius . Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b].

Use integration to find the area of the triangle with the given vertices. (0, 0), (1, 9), (4, 2)

Evaluate the limit by interpreting it as the limit of a Riemann sum of a function on the interval [a, b].

Find the integral.

Sketch the region bounded by the graphs of the given equations and find the area of that region. y = -x² + 4, y = 6x + 5

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle. y = 25 - x², y = 0; the line

Find the volume of the frustum of a pyramid with square base of side square top of side and height

Find the indefinite integral.

Find the integral.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 5: Applications of Integration

Find the values of c such that the area of the region bounded by the parabolas is .

Sketch the region bounded by the graphs of the given equations and find the area of their region. x = y2 + 2, x = y - 2, y = -3, y = 3

Find the area of the region bounded by the given curves.

Find the integral.

Evaluate the integral using an appropriate trigonometric substitution.

Find the area of the region bounded by the curves.

Find the integral.

Evaluate the integral.

Find the integral using an appropriate trigonometric substitution.

The base of a solid is a circular disk with radius . Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b].

Use integration to find the area of the triangle with the given vertices. (0, 0), (1, 9), (4, 2)

Evaluate the limit by interpreting it as the limit of a Riemann sum of a function on the interval [a, b].

Find the integral.

Sketch the region bounded by the graphs of the given equations and find the area of that region. y = -x2 + 4, y = 6x + 5

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle. y = 25 - x2, y = 0; the line

Find the volume of the frustum of a pyramid with square base of side square top of side and height

Find the indefinite integral.

Find the integral.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Sketch the region bounded by the graphs of the given equations and find the area of their region. x = y² + 2, x = y - 2, y = -3, y = 3

Sketch the region bounded by the graphs of the given equations and find the area of that region. y = -x² + 4, y = 6x + 5

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle. y = 25 - x², y = 0; the line