What is the integral from 0 to 2 of integral from 3y to 6 of 5e^{x^2} ?

The integral from 0 to 2 of integral from 3y to 6 of 5e^{x^2} is (5(e^{36}-1))/6

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integral from 0 to 2 of integral from 3y to 6 of 5e^{x^2}

\int_{0}^{2} \int_{3 y}^{6} 5 e^{x^{2}} d x d y

\frac{5 ( e ^{36} - 1 )}{6}

Decimal

3.59269 E 15

Solution steps

\int_{0}^{2} \int_{3 y}^{6} 5 e^{x^{2}} d x d y

Change order of integration

= \int_{0}^{6} \int_{0}^{\frac{x}{3}} 5 e^{x^{2}} d y d x

\int_{0}^{\frac{x}{3}} 5 e^{x^{2}} d y = \frac{5 x e ^{x^{2}}}{3}

= \int_{0}^{6} (\frac{5 x e ^{x^{2}}}{3}) d x

\int_{0}^{6} (\frac{5 x e ^{x^{2}}}{3}) d x = \frac{5 ( e ^{36} - 1 )}{6}

= \frac{5 ( e ^{36} - 1 )}{6}

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What is the integral from 0 to 2 of integral from 3y to 6 of 5e^{x^2} ?
The integral from 0 to 2 of integral from 3y to 6 of 5e^{x^2} is (5(e^{36}-1))/6