# Evaluate: ∫ ( 1 − X ) √ X D X - Mathematics

Sum

Evaluate: $\int\left( 1 - x \right)\sqrt{x}\text{ dx }$

#### Solution

$\int\left( 1 - x \right)\sqrt{x} dx = \int\left( \sqrt{x} - x\sqrt{x} \right) dx$
$= \int\left( x^\frac{1}{2} - x^\frac{3}{2} \right) dx$
$= \frac{x^\frac{1}{2} + 1}{\frac{1}{2} + 1} - \frac{x^\frac{3}{2} + 1}{\frac{3}{2} + 1} + c$
$= \frac{2}{3} x^\frac{3}{2} - \frac{2}{5} x^\frac{5}{2} + c$
$\text{ Hence,} \int\left( 1 - x \right)\sqrt{x} \text{ dx }= \frac{2}{3} x^\frac{3}{2} - \frac{2}{5} x^\frac{5}{2} + c$
Concept: Evaluation of Simple Integrals of the Following Types and Problems
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 54 | Page 198
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