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Evaluate the given double integrals.$$\int_{1}^{2} \int_{0}^{x} y x^{3} e^{x^{2}} d y d x$$

$\frac{e^{8}-7-e}{6}$

Calculus 3

Chapter 29

Partial Derivatives and Double Integrals

Section 4

Double Integrals

Partial Derivatives

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we want to evaluate the devil and drill given. Ask the integral from 1 to 2. At the integral from zero to X Y X Q E to the X Y squared Dy Ds. This question is shown on the r standpoint or understanding of integration From the standpoint of Multivariate calculus. We're going to solve in two steps. In each step we use single variable integration techniques where in step one we can do the inner integral here that zero X Y x q V x Y squared do I. And then in step two we evaluate the outer integral from 1 to 2 D X. Using our results from step one as our instagram. So proceeding us all we have are double integral is equal to the integral from zero to of half X squared E v xy squared zero X dx or the integral from zero to have X squared and x cubed minus half X squared dx. Thus we can evaluate our solution ask 1 60 x cubed minus 16 Excuse from 0 to 2 or other final solution. Each of the eight minus nine divided by six.

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