Evaluate ∫₀^1 x e^x^2 dx.

Definite Integrals & Area · Question 19 of 71

Question 19

MediumOriginal question

Evaluate $\int_{0}^{1} x e^{x^{2}}\,dx$ .

\frac{1}{2} - \frac{e}{2}

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- \frac{1}{4} + \frac{e}{4}

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- \frac{1}{2} + \frac{e}{2}

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\frac{e}{2}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

An antiderivative is $F(x) = \frac{e^{x^{2}}}{2}$ .
By the fundamental theorem, the integral is $F(1) - F(0) = - \frac{1}{2} + \frac{e}{2}$ .

Worth noting

$\frac{e}{2}$ is $F(1)$ alone: $F(0)$ was not subtracted.

Ten questions from Definite Integrals & Area, at your own pace.

Ten questions from Definite Integrals & Area, at your own pace.