Area lying in the first quadrant and bounded by the circle x2+y2=4 and the lines x=0 and x=2 is
\(\pi\)
- \(\frac{π}{2}\)
- \(\frac{π}{3}\)
- \(\frac{π}{4}\)
The Correct Option is A
Solution and Explanation
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.
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