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Q.

The line x=π4 divides the area of the region bounded by y = sinx, y = cos x and x-axis 0xπ2 into two regions of areas A1 and A2. Then A1:A2=

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a

4 :1

b

3 :1

c

2 :1

d

1 : 1

answer is D.

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Detailed Solution

y=sinx, y=cosxx=x=0,x=π/2

A1=0π4cosxsinxdx=(sinx+cosx)0π2=21

 

A2=π4π/2sinxcosxdx=(cosxsinx)π/4π/2=(1)1212=12=21

A1:A2=2  -1:2  -1=1:1

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The line x=π4 divides the area of the region bounded by y = sinx, y = cos x and x-axis 0≤x≤π2 into two regions of areas A1 and A2. Then A1:A2=