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Let F:RtoR be a thrice differntiable fun...

Let `F:RtoR` be a thrice differntiable function. Suppose that `F(1)=0,F(3)=-4` and `F'(x)lt0` for all `x epsilon(1,3)`. Let `f(x)=xF(x)` for all `x inR`. Then the correct statement(s) is (are)

A

(a) `9 f'(3) +f' (1) -32 =0`

B

(b) `int_(1)^(3)f(x) dx=12`

C

(c) `9 f' (3) - f'(1)+32=0`

D

(d) `int_(1)^(3)f(x) dx =-12`

Text Solution

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The correct Answer is:
C, D
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
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  3. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  13. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

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  17. Which of the following is true?

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