₀¹ x e^x dx = 1 - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Prove the following (Exercises 262 to 267)

Question : 263 of 271

Marks: +1, -0

\int\limits_{0}^{1} x e^x dx = 1

Solution:

Let

I = \int\limits_{0}^{1} x e^x dx

Integrating by parts, we get

\left[ x \int e^x dx - \int \left( \frac{d}{dx} x \int e^x dx \right) dx \right]_{0}^{1}

= \left[ x \int e^x - \int e^x dx \right]_{0}^{1}

= \left[ x e^x - e^x \right]_{0}^{1}

= \left[ (e-0) - (e-1) \right] = 1

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