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Question
The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 ≤ x ≤ `pi/2` is ______.
Options
`sqrt(2)` sq.units
`(sqrt(2) + 1)` sq.units
`(sqrt(2) - 1)` sq.units
`(2sqrt(2) - 1)` sq.units
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Solution
The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 ≤ x ≤ `pi/2` is `(sqrt(2) - 1)` sq.units.
Explanation:
Given that y-axis, y = cos x, y = sin x, 0 ≤ x ≤ `pi/2`
Required area = `int_0^(pi/4) cos x "d"x - int_0^(pi/4) sin x "d"x`
= `[sin x]_0^(pi/4) - [- cos x]_0^(pi/4)`
= `[sin pi/4 - sin 0] + [cos pi/4 - cos 0]`
= `[1/sqrt(2) - 0 + 1/sqrt(2) - 1]`
= `2/sqrt(2) - 1`
= `(sqrt(2) - 1)` sq.units
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