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Question
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Options
`pi`
`pi/2`
`pi/3`
`pi/4`
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Solution
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is π.
Explanation:
Equation of a circle x2 + y2 = 4
Required ocean = Ocean of OAB
`= int_0^2 y dx`
`= int_0^2 sqrt(4 - x^2) dx [(because x^2 + y^2 = 4),(=> y = sqrt(4 - x^2))]`
`= [x/2 sqrt(4 - x^2) + 4/2 sin^-1 x/2]_0^2`
`= [0 + 2 sin^-1 (1)] - (0 + 0)`
`= 2 xx pi/2`
= π Units
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