Let f:[–1,2]→[0,∞) be a continuous function such that f(x)=f(1–x) for all x∈[–1,2]. Let R1=2∫−1xf(x)dx, and R2 be the area of the region bounded by y=f(x),x=–1,x=2, and the x−axis. Then
A
R1=2R2
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B
3R1=R2
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C
2R1=R2
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D
R1=3R2
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Solution
The correct option is C2R1=R2 We have, R1=2∫−1xf(x)dx=2∫−1(1−x)f(1−x)dx =2∫−1f(1−x)dx−2∫−1xf(1−x)dx =R2−R1 ⇒2R1=R2