Question

Area lying in the first quadrant and bounded by the circle x²+y²=4 and the lines x=0 and x=2 is

• A. \(\pi\)
• B. \(\frac{π}{2}\)
• C. \(\frac{π}{3}\)
• D. \(\frac{π}{4}\)

Answer 1

The Correct Option is A

The correct option is(A): \(\pi\).

The area bounded by the circle and the lines, x=0 and x=2, in the first quadrant is

represented as

∴Area OAB=\(∫_0^20y dx\)

=\(∫_0^2√4-x^2dx\)

=\([\frac{x}{2}\sqrt{4-x^2}+\frac{4}{2}sin^{-1}\frac{x}{2}]_0^2\)

=\(2(\frac{π}{2})\)

=π units

Thus, the correct answer is A.