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The area enclosed by the curve y=sinx+co...

The area enclosed by the curve `y=sinx+cosxa n dy=|cosx-sinx|` over the interval `[0,pi/2]` is `(a)4(sqrt(2)-2)` (b) `2sqrt(2)` (`sqrt(2)` -1) `(c)2(sqrt(2)` +1) (d) `2sqrt(2)(sqrt(2)+1)`

A

`4(sqrt2-1)`

B

`2sqrt2(sqrt2-1)`

C

`2(sqrt2+1)`

D

`2sqrt2(sqrt2+1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Required area `=underset(0)overset(pi//4)int |2sin x|dx+underset(pi//4)overset(pi//2)int |2 cos x|dx=2sqrt2(2sqrt2-1)`
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