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Question
The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is ______.
Options
8 sq.units
20π sq.units
16π sq.units
256π sq.units
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Solution
The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is 8 sq.units.
Explanation:
Here, equation of curve is y = `sqrt(16 - x^2)`
Required area = `2[int_0^4 sqrt(16 - x^2) "d"x]`
= `2[x/2 sqrt(16 - x^2) + 16/2 sin^-1 x/4]_0^4`
= `2[(0 + 8 sin^-1 4/4) - (0 + 0)]`
= `2[8sin^-1 (1)]`
= `16 * pi/2`
= 8 sq.units.
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