If f is a continuous function in the interval [a, b], then the value of ∫10f((b−a)x+a)dx is equal to
A
(b−a)∫baf(x)dx
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B
(a−b)∫baf(x)dx
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C
1(b−a)∫baf(x)dx
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D
1(a−b)∫abf(x)dx
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Solution
The correct options are C1(b−a)∫baf(x)dx D1(a−b)∫abf(x)dx We have, ∫10f((b−a)x+a)dxLet(b−a)x+a=t⇒dx=dtb−a.Also,whenx=0,t=aand,whenx=1,t=b.∴∫10f((b−a)x+a)dx=∫baf(t)dtb−a=1b−a∫baf(x)dx=−1a−b∫baf(x)dx=1a−b∫abf(x)dx