First slide

Evaluation of definite integrals

Question

The value of $\int_{- π / 2}^{π / 2} (x^{3} + xcos x + \tan^{5} x + 1) dx$ is

Moderate

A

0
B

2
C

$π$
D

1

Solution

Let
$\begin{array}{l} I = \int_{- π / 2}^{π / 2} (x^{3} + xcos x + \tan^{5} x + 1) dx \\ \Rightarrow I = \int_{- π / 2}^{π / 2} x^{3} dx + \int_{- π / 2}^{π / 2} xcos xdx + \int_{- π / 2}^{π / 2} \tan^{5} xdx + \int_{- π / 2}^{π / 2} 1 dx \end{array}$
we know that, $\int_{- a}^{a} f (x) dx = \{\begin{array}{cc} 2 \int_{0}^{a} f (x) dx, & if f (x) is even \\ 0, & if f (x) is odd \end{array}$
$\begin{array}{l} ∴ l = 0 + 0 + 0 + 2 \int_{0}^{π / 2} 1 dx \\ [∵ x^{3}, xcos x and \tan^{5} (x) are odd functions] \end{array}$
$∴ I = 2 [x]_{0}^{π / 2} = \frac{2 π}{2} = π$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App