First slide

Area of bounded Regions

Question

$If f (x) = min (| x |, 1 - | x |, \frac{1}{4}) \forall x \in R then find the value of \int_{- 1}^{1} f (x) d x .$

Difficult

A

$\frac{3}{2}$
B

$\frac{3}{4}$
C

3
D

$\frac{3}{8}$

Solution

$f (x) = min (| x |, 1 - | x |, \frac{1}{4})$
Now, from figure, we have
$\int_{- 1}^{1} f (x) d x = 2 (Area of trapezium O A B C)$
$\begin{matrix} = 2 \times \frac{1}{2} \times (A B + O C) \times A M \\ = 2 (\frac{1}{2} (1 + \frac{1}{2}) \frac{1}{4}) = \frac{3}{8} \end{matrix}$

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