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Application of Integration

Section: Mathematics

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Question : 17

Total: 28

Let F:R→R be a thrice differentiable function. Suppose that F(1)=0, F(3)=−4 and F′(x)<0 for all x∊(

,3). Let f(x)=xF(x) for all x∊R.

If

x2F′(x)dx=−12 and

x3F"(x)dx=40,then the correct expression(s) is (are)

[JEE Adv 2015 P2]

9f′(3)+f′(1)−32=0
3
∫
1
f(x)dx=12
9f′(3−f′(1)+32=0
3
∫
1
f(x)dx=−12

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