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Application of Integration question

2015 · Shift 2 · Q37

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PYQ Library
JEE Advanced
Mathematics
Application of Integration
2015 · Shift 2 · Q37

Application of Integration question

2015 · Shift 2 · Q37

JEE AdvancedMathematicsApplication of IntegrationMultiple correct+4 / −1

Let

F:R \to R

be a thrice differentiable function. Suppose that

F\left( 1 \right) = 0,F\left( 3 \right) = - 4

and

F\left( x \right) \lt 0

for all

x \in \left( {{1 \over 2},3} \right).

Let

f\left( x \right) = xF\left( x \right)

for all

x \in R.

If

\int_1^3 {{x^2}F'\left( x \right)dx = - 12}

and

\int_1^3 {{x^3}F''\left( x \right)dx = 40,}

then the correct expression(s) is (are)

A
$9f'\left( 3 \right) + f'\left( 1 \right) - 32 = 0$
B
$\int_1^3 {f\left( x \right)dx = 12}$
C
$9f'\left( 3 \right) - f'\left( 1 \right) + 32 = 0$
D
$\int_1^3 {f\left( x \right)dx = -12}$

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