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The area enclosed between the curve y=si...

The area enclosed between the curve `y=sin^(2)x and y=cos^(2)x` in the interval `0le x le pi` is _____ sq. units.

A

2 sq unit

B

`(1)/(2)` sq unit

C

1 sq unit

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`y=sin^(2)xand y=cso^(2)x`
Solving `sin^(2)x=cos^(2)x`
`therefore" "x=pi//4,3pi//4`
Graph of functions is as shown in the following figure.

From the figure, the required area
`=int_(pi//4)^(3pi//4)(sin^(2)x-cos^(2)x)dx`
`=-int_(pi//4)^(3pi//4)cos2xdx=1`
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Knowledge Check

  • The area enclosed by the curve |x| + |y| = 1 is

    A
    2
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