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The area of the region bounded by the Y-...

The area of the region bounded by the `Y-"axis"` `y = "cos" x` and `y = "sin" x` Where `0lexlepi/2,` is

A

`sqrt2" sq units"`

B

`(sqrt2+1)" sq units"`

C

`(sqrt2-1)" sq units"`

D

`(2sqrt2-1)" sq units"`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, Y-axis i.e., x = 0, y =cos x and y = sin x, where `0lexlepi/2`.

`:. " Required area "=int_(0)^(pi//4)(cosx-sinx)dx`
`=[sin]_(0)^(pi//4)+[cosx]_(0)^(pi//4)`
`(sin .pi/4-sin0)+(cos.pi/4-cos0)`
`(1/sqrt2+1/sqrt2)-1`
`=-1+2/sqrt2=(-sqrt2+2)/sqrt2`
`=(-2+2sqrt2)/2=(sqrt2-1)"sq units"`
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