int_{3}^{8} x e^{x^{2}} d x

Question

Accepted Answer

Step:1 ：Define the function (f = x e^{x^{2}})Step:2 ：Calculate the indefinite integral of the function, which is (int f dx = frac{e^{x^{2}}}{2})Step:3 ：Substitute the limits of integration into the indefinite integral to calculate the definite integral, which is (int_{3}^{8} f dx = frac{e^{64}}{2} - frac{e^{9}}{2})Step:4 ：The definite integral from 3 to 8 of the function (x e^{x^{2}}) is (boxed{-frac{e^{9}}{2} + frac{e^{64}}{2}})

Answer

Step: 1 ：Define the function (f = x e^{x^{2}})Step: 2 ：Calculate the indefinite integral of the function, which is (int f dx = frac{e^{x^{2}}}{2})Step: 3 ：Substitute the limits of integration into the indefinite integral to calculate the definite integral, which is (int_{3}^{8} f dx = frac{e^{64}}{2} - frac{e^{9}}{2})Step: 4 ：The definite integral from 3 to 8 of the function (x e^{x^{2}}) is (boxed{-frac{e^{9}}{2} + frac{e^{64}}{2}})

$\int_{3}^{8} x e^{x^{2}} d x$

Answer

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$\int_{3}^{8} x e^{x^{2}} d x$