COMPASSLearning

Talk to us Register Login

CBSE Class 12 · 2012 · Indefinite IntegralsVery Short Answer

Evaluate :

\int (1 - x) x d x

Answer: $\frac{2}{3} x^{3/2} - \frac{2}{5} x^{5/2} + C$

Solution

Expand the integrand into powers of

x

:

(1 - x) x = x^{1/2} - x^{3/2} .

Integrating with the power rule,

\int x^{1/2} d x - \int x^{3/2} d x = \frac{2}{3} x^{3/2} - \frac{2}{5} x^{5/2} + C .

\frac{2}{3} x^{3/2} - \frac{2}{5} x^{5/2} + C

CBSE Class 12 Board · 2012 · Subjective

Practise more: all CBSE board PYQs on Indefinite Integrals →

More board questions on Indefinite Integrals

The integral $\int \frac{d x}{9 - 4 x ^{2}}$ is equal to
CBSE 2024View solution →
Find $\int cos^{3} x e^{l o g s i n x} d x$
CBSE 2024View solution →
Find $\int \frac{2 x + 1}{( x + 1 ) ^{2} ( x - 1 )} d x$
CBSE 2024View solution →
Anti-derivative of $\frac{tan x - 1}{tan x + 1}$ with respect to $x$ is:
CBSE 2023View solution →
Find $\int \frac{s i n ^{- 1} x}{( 1 - x ^{2} ) ^{3/2}} d x$
CBSE 2023View solution →
Evaluate $\int e^{x} (\frac{1 - s i n x}{1 - c o s x}) d x$
CBSE 2023View solution →