First slide

Evaluation of definite integrals

Question

_{$\int_{0}^{1} x {(1 - x)}^{10} d x =$}

Easy

A

_{$\frac{1}{112}$}
B

_{$\frac{1}{132}$}
C

_{$\frac{1}{246}$}
D

_{$\frac{1}{92}$}

Solution

_{$I = \int_{0}^{1} x {(1 - x)}^{10} d x$}
_{$= \int_{0}^{1} (1 - x) . x^{10} d x = \int_{0}^{1} (x^{10} - x^{11}) d x$}

_{$= \frac{1}{132}$}

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