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Question

If baf(x)f(a)+f(a+bx)dx=10, then

A
b=22,a=2
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B
b=15,a=5
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C
b=10,a=10
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D
b=10,a=2
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Solution

The correct options are
A b=15,a=5
B b=10,a=10
D b=22,a=2

To find a and b

We know that

baf(x)dx=baf(a+bx)dxI=baf(x)f(x)+f(a+bx)dx=baf(a+bx)f(a+bx)+f(a+b(a+bx))dx

I=baf(a+bx)f(a+bx)+f(x)dxI+I=baf(x)f(x)+f(a+bx)dx+baf(a+bx)f(a+bx)+f(x)dx

2I=baf(x)+f(a+bx)f(x)+f(a+bx)dx2I=ba1.dx=[x]ba=baI=12(ba)

Given that, 12(ba)=10

ba=20

Hence the correct answer are those which (ba)=20

A,B and C are correct.


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