Definite Integration Question 437

Question: The area of the region in 1st quadrant bounded by the y-axis, y = $ \frac{x}{4} $ , y = 1 + $ \sqrt{x} $ , and $ y=\frac{2}{\sqrt{x}} $ is

Options:

A) 1

B) 2

C) $ \pi $

D) 2 $ \pi $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] The required area is shown by shaded portion in the figure.

The required area is $ A=\int\limits _{-\pi /2}^{\pi /2}{| \sin y |dy=2\int\limits_0^{\pi /2}{\sin ydy=2}} $