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Question
Area of the region bounded by the curve y = cosx between x = 0 and x = π is ______.
Options
2 sq.units
4 sq.units
3 sq.units
1 sq.units
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Solution
Area of the region bounded by the curve y = cosx between x = 0 and x = π is 2 sq.units.
Explanation:
Given that: y = cos x, x = 0, x = π
Required area = `int_0^(pi/2) cos x "d"x + |int_(pi/2)^pi cos x "d"x|`
= `[sin x]_0^(pi/2) + |(sin x)_(pi/2)^pi|`
= `[sin pi/2 - sin 0] + |[sin pi - sin pi/2]|`
= `(1 - 0) + |0 - 1|`
= 1 + 1
= 2 sq.units
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