Problem 61:
http://25.media.tumblr.com/c70ad4d8ea89e…
The answer on the back of the book says it's 3.
http://25.media.tumblr.com/c70ad4d8ea89e…
The answer on the back of the book says it's 3.
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let x(θ) = 2sinθ
dx = 2cosθ dθ
(1/2) ∫[0,π/2] f(2sinθ) (2cosθ dθ)
Range changes:
x(0) = 2sin(0) = 0
x(π/2) = 2sin(π/2) = 2
(1/2) ∫[0,2] f(x) dx
= (1/2) * 6 = 3
dx = 2cosθ dθ
(1/2) ∫[0,π/2] f(2sinθ) (2cosθ dθ)
Range changes:
x(0) = 2sin(0) = 0
x(π/2) = 2sin(π/2) = 2
(1/2) ∫[0,2] f(x) dx
= (1/2) * 6 = 3