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Please solve RD Sharma class 12 Chapter Definite integrals exercise 19.2 question 7 maths textbook solution.

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Hint: We use indefinite integral formula then put limits to solve this integral.

Given: \int_{0}^{1} x e^{x^{2}} d x

Solution: I=\int_{0}^{1} x e^{x^{2}} d x

Put x^2=t

2x\; \; dx=dt


When x=0  then t=0  and when x=1  then t=1

\begin{aligned} &I=\int_{0}^{1} x e^{t} \frac{d t}{2 x} \\ &=\frac{1}{2} \int_{0}^{1} e^{t} d t \end{aligned}

=\frac{1}{2}[e^t]_0^1                                             [\int e^t\; dt =e^t+c]



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