Calc 2 Exam 1

Question 1

Area Between Curves, X axis

Accepted Answer

$A = \int_a^b [f(x)-g(x)] dx$

Question 2

Area Between Curves, Y axis

Accepted Answer

$A = \int_c^d [f(y)-g(y)]dy$

Question 3

Disk Method, X Axis

Accepted Answer

$V = \pi \int_a^b [R(x)]^2 dx$

Question 4

Disk Method, Y Axis

Accepted Answer

$V= \pi \int_c^d [R(y)]^2 dy$

Question 5

Washer Method, X Axis

Accepted Answer

$V = \pi \int_a^b [R(x)^2 - r(x)^2] dx$

Question 6

Washer Method, Y Axis

Accepted Answer

$V = \pi \int_c^d [R(y)^2 - r(y)^2] dy$

Question 7

Shell Method, X axis

Accepted Answer

$V = 2\pi \int_a^b p(x)h(x) dx$

Question 8

Shell Method, Y axis

Accepted Answer

$V = 2\pi \int_c^d p(y)h(y) dy$

Question 9

Arc Length of a Curve, X axis

Accepted Answer

$s = \int_a^b \sqrt{1 + [f'(x)]^2]}dx$

Question 10

Arc Length of a Curve, Y axis

Accepted Answer

$s = \int_c^d \sqrt{1 + [g'(y)]^2]}dy$

Question 11

Surface Area of a Surface of Revolution, X Axis

Accepted Answer

$s=2\pi \int_a^b r(x) \sqrt{1+[f'(x)]^2}$

Question 12

Surface Area of a Surface of Revolution, Y Axis

Accepted Answer

$s=2\pi \int_c^d r(y) \sqrt{1+[g'(y)]^2}$

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