Cal 2 final exam

Question 1

Average value

Answer 1

1/(b-1)∫f(x)dx

Question 2

Area

Answer 2

∫|f(x)-g(x)|dx, where f(x) is the top function

Question 3

Volume

Answer 3

∫A(x)dx, where A(x) = ΠR^2m where R is the radius of the circle that we are rotating around the axis

Question 4

Trig sub

Answer 4

(a^2-x^2)^1/2 = asinΘ
(a^2+x^2)^1/2 = atanΘ
(x^2-a^2)^1/2 = asecΘ

Question 4

Trig sub

Answer 4

(a^2-x^2)^1/2 = asinΘ
(a^2+x^2)^1/2 = atanΘ
(x^2-a^2)^1/2 = asecΘ

Question 5

Arc length

Answer 5

L = ∫(1+(dx/dy)^2)^1/2dx

Question 6

Area of a surface of revolution

Answer 6

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