Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Application of Integrals

Question:

The area of the region described by A = {(x, y) : x2 + y2 \(\leq\) 1 and y2 \(\leq\) 1 - x} is : 

Options:

\(\frac{\pi}{2} + \frac{4}{3} \)

\(\frac{\pi}{2} - \frac{4}{3} \)

\(\frac{\pi}{2} - \frac{2}{3} \)

\(\frac{\pi}{2} + \frac{2}{3} \)

Correct Answer:

\(\frac{\pi}{2} + \frac{4}{3} \)

Explanation:

A = \(\frac{1}{2}  \pi + 2\int_{0}^{1}\sqrt{1 - x} dx\)

   = \(\frac{\pi}{2} + \frac{4}{3} \)