Question

The area enclosed by the curves `y=sinx+cosx and y=|cosx−sinx|` over the interval `[0,pi/2]` is (a) `4(sqrt2-1)` (b) `2sqrt2(sqrt2-1)` (c) `2(sqrt2+1)` (d) `2sqrt2(sqrt2+1)`
A. `4(sqrt(2)-1)`
B. `2sqrt(2)(sqrt(2)-1)`
C. `2(sqrt(2)+1)`
D. `2sqrt(2)(sqrt(2)+1)`

Answer 1

Correct Answer - B
Since `sin x and cos x gt 0" for "x in [0,pi//2],` the graph of y= sin x+cos x always lies above the graph of `y=|cos x - sin x|`
Also `cos x gt sin x" for " x in [0,pi//4] and sin gt cos" for " x in [pi//4,pi//2]`
`rArr" Area "=overset(pi//4)underset(0)int((sin x + cos x)-(cos x - sin x))dx+overset(pi//2)underset(pi//4)int((sin x + cos x)-(sin x - cos x))dx`
`=4-2sqrt(2)`