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D is the planar region bounded by y = 0, y = x² and x = 1. Find the value of the integral below.​

D is the planar region bounded by y = 0, y = x² and x = 1. Find the value of the integral below.​
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D is the planar region bounded by y = 0, y = x² and x = 1. Find the value of the integral below.​

D is the planar region bounded by y = 0, y = x² and x = 1. Find the value of the integral-example-1
User Yantrab
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\displaystyle \iint_D x e^y \, dA = \int_0^1 \int_0^(x^2) x e^y \, dy \,dx \\\\ ~~~~~~~~ = \int_0^1 x (e^(x^2) - 1)\, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 e^u \, du - \int_0^1 x \,dx = \boxed{\frac{e - 2}2}

User Emsr
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