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riversmom

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posted by riversmom on 11/4/2009 2:32:14 PM | status: Closed | Earned Karma: 25

double integral

Course	Textbook	Chapter	Problem	Needs by
Calculus	Calculus: Several Variables (9th) by Salas, Hille, Etgen	16.3	49E	11/4/2009 at 11:00:00 PM

Question Details:

Can someone please help me work this out? I'm new at these double integrals. Thanks!

Evaluate the double integral:

Thanks!

Tags: Calculus, Calculus, Calculus: Several Variables (9th)

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Answers:

anonymousx...

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posted by anonymousxyz on 11/4/2009 2:44:17 PM | status: Live

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$\text{Reverse the order of integration:}$

$\begin{align*} \int_0^1 \int_x^1 x^2 e^{y^4} \;\text{d}y\,\text{d}x &= \int_0^1 \int_0^y x^2 e^{y^4} \;\text{d}x\,\text{d}y \\\\&= \int_0^1\frac{x^3 e^{y^4}}3 \;\bigg|_0^y \;\text{d}y \\\\&= \int_0^1\frac{y^3 e^{y^4}}3\;\text{d}y \\\\&= \frac{e^{y^4}}{12}\;\bigg|_0^1 \\\\&= \frac{e - 1}{12} \end{align*}$

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