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Question

If f is a continuous function in the interval [a, b], then the value of 10 f((ba)x+a) dx is equal to

A
(ba)ba f(x) dx
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B
(ab)ba f(x) dx
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C
1(ba)ba f(x) dx
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D
1(ab)ab f(x) dx
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Solution

The correct options are
C 1(ba)ba f(x) dx
D 1(ab)ab f(x) dx
We have,
10 f((ba)x+a) dxLet (ba)x+a=tdx=dtba.Also, when x=0, t=a and,when x=1, t=b.10 f((ba)x+a) dx=ba f(t) dtba =1baba f(x) dx=1abba f(x) dx=1abab f(x) dx

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