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Consider the curves y= sin x and y = cos...

Consider the curves `y= sin x and y = cos x.` What is the area of the region bounded by the above two curves and the lines `x = 0 and x =pi/4.`

A

`sqrt(2) - 1`

B

`sqrt(2) + 1`

C

`sqrt(2)`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
A

Area of shaded region `= int_(0)^(pi/4) (cos x - sin x) dx`
`= [sinx + cos x]_(0)^(pi/4)`
`= [(1/(sqrt(2)) + 1/(sqrt(2))) - (0+1)]`
`( sqrt(2)- 1)` sq. units
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