Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

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

Advertisement Remove all ads

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
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 54 | Page 198
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×