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Q.

Let A1 be the area of the region bounded by the curves y=sinx,y=cosx and y- cois in the first quadrant. Also, let A2 be the area of the region bounded by the curves y=sinx,y=cosx,x- cois and x=π2 in the first quadrant. Then

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a

2A1=A2 and A1+A2=1+2

b

A1:A2=1:2 and A1+A2=1

c

A1:A2=1:2 and A1+A2=1

d

A1=A2 and A1+A2=2

answer is C.

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Detailed Solution

y=sinx,y=cosx,y=axisA1=∫0π/4(cosx-sinx)dx=(sinx+cosx)0π/4=2-1y=sinx,y=cosx,x- axis, x=π/2A2=∫0π/4sinxdx+∫π/4π/2cosx=-(cosx)0π/4+(sinx)π/4π/2=1-12+1-12=2-2A1:A2=2-1:2(2-1)=1:2A1+A2=1

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Let A1 be the area of the region bounded by the curves y=sinx,y=cosx and y- cois in the first quadrant. Also, let A2 be the area of the region bounded by the curves y=sinx,y=cosx,x- cois and x=π2 in the first quadrant. Then