# Calc

Evaluate the integral by reversing the order of integration.

(2 integrations)
0 to 1
sqrt(x) to 1

8(y^3+1) dy dx

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1. ∫[0,1]∫[√x,1] 8(y^3+1) dy dx
= ∫[0,1]8(y^4/4+y)|[√x,1] dx
= ∫[0,1]8[(1/4+1)-(x^2/4+√x)] dx
= ∫[0,1] -2x^2 - 8√x + 10 dx
= (-2/3 x^3 - 16/3x^(3/2) + 10x [0,1]
= -2/3 - 16/3 + 10
= 4

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