Exam #1 Review

Question 1

Area under a curve

Answer 1

Integral from a to b of f(x)dx

Question 2

Area between curves with respect to x

Answer 2

Integral from a to b of [f(x)-g(x)]dx

Question 3

Area between curve with respect to y

Answer 3

Integral from a to b of [f(y)-g(y)]dy

Question 4

Axis rotation volume: Disk method with respect to x

Answer 4

V= (pi) Integral from a to b of [f(x)]^2 dx

Question 5

Axis rotation volume: Disk method with respect to y

Answer 5

V=(pi) Integral from a to b of [f(y)]^2 dy

Question 6

Axis rotation volume: Washer method with respect to x

Answer 6

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

Question 7

Axis rotation volume: Washer method with respect to y

Answer 7

V=(pi) Integral from a to b of ([f(y)]^2)-([g(y)]^2) dy

Question 8

Non axis rotation volume: Disk method with respect to x

Answer 8

V=(pi) Integral from a to b of ([R(x)-c]^2) dx

Question 9

Non axis rotation volume: Disk method with respect to y

Answer 9

V=(pi) Integral from a to b of ([R(y)-c]^2) dy

Question 10

Non axis rotation volume: Washer method with respect to x

Answer 10

V=(pi) Integral from a to b of ([R(x)-c]^2)-([r(x)-c]^2) dx

Question 11

Non axis rotation volume: Washer method with respect to y

Answer 11

V=(pi) Integral from a to b of ([R(y)-c]^2)-([r(y)-c]^2) dy