Calculus II Test 1 6.2-6.7

Question 1

Area of a region bounded by f(x) and g(x) on [a,b]

Answer 1

integral from a to b of (g(x)-f(x)) where f(x)

Question 2

volume by slices

Answer 2

integral from a to b of A(x)dx

Question 3

Disk method

Answer 3

integral from a to b of (pi(f(x))^2)dx

Question 4

Washer method

Answer 4

integral from a to b of (pi)[(f(x)^2-(g(x))^2]dx

Question 5

Volume by shells

Answer 5

integral from a to b of (2pix*f(x))dx

Question 6

Volume by shells with 2 equations

Answer 6

integral from a to b of (2pix*(f(x)-g(x))dx where f(x)>g(x)

Question 7

Length of a curve

Answer 7

integral from a to b of (sqrt(1+(f’(x))^2))dx

Question 8

disk and washer method revolved about the x-axis, integrate with respect to…

Answer 8

x

Question 9

Area of a surface of revolution

Answer 9

integral of a to b (2pief(x)*sqrt(1+f’(x)^2))dx

Question 9

Shell method to find volume of solids

Answer 9

2pi(x+d)(f(x)-g(x))dx where it’s revolved around the line -d

Question 10

Integral of e^(ax)

Answer 10

(e^ax)/a

Question 11

Integral of 1/x

Answer 11

Ln(|x|)