# 15

Find the volume of the following solid.

The solid between the cylinder fixy) and the region R-[(xy): 0≤x≤ In 6, -2≤y≤2).

The volume of the solid is

(Type an exact answer.)

# 16

Find the volume of the given solid over the indicated region of integration.

f(x,y) = 2x+4y+3; R=((x,y): -3≤x≤2, 2sys4}

What is the volume of the region?

3

units

fix y)=zk

# 17

Let R = {(x,y): 0≤x≤x, 0≤ysa). For what values of a, with Osasz, is sin(x + y) dA equal to 17

R

a=

(Type an exact answer, using as needed. Use a comma to separate answers as needed.)/n# 18

Evaluate the following integral as it is written.

# 19

3xy dy dx

3xy dy dx =

Evaluate the following integral as it is written.

2x/3 sigx

JJ dy dx

x/4 cos x

2x/3 sigx

(Simplify your answer.)

dy dx=

4 cosx

(Type an exact answer, using radicals as needed.)

# 20

Evaluate the following integral, where R is bounded by x = 3, y = 2x+2, and y=-x-1.

SS y² dA

R

²-(Simplify your cur/n# 21

Evaluate the following integral.

KIMO

IM0

9y sin y

0

gy sin y

dx dy

dx dy = (Type an exact answer, using it as needed.)

# 22

Find the volume of the following solid.

The tetrahedron bounded by the coordinate planes (x = 0, y = 0, z = 0) and the plane 2x + 7y+z-14=0

The volume is

(Simplify your ansv

cubic units.

units.

square units.

fraction.)/n# 23

Reverse the order of integration in the following integral.

KIN

# 24

U

sin

SIN

f(x,y) dx dy

Reverse the order of integration.

An

JT f(x,y) dy dx

00

(Type exact answers, using x as needed.)

Reverse the order of integration and evaluate the integral.

HA

dy dx

II)-

The reversed order of integration is

(Simplify your answers.)

dx dy./n# 25

Use double integrals to compute the area of the region bounded by the parabola y=x²

and the line y = 4.

The area is

(Simplify your ar

square units.

cubic units.

units