jee-advanced 2015 Q60

jee-advanced · India · paper2 Indefinite & Definite Integrals Definite Integral Evaluation (Computational)

If $\int _ { 1 } ^ { 3 } x ^ { 2 } F ^ { \prime \prime } ( x ) d x = - 12$ and $\int _ { 1 } ^ { 3 } x ^ { 3 } F ^ { \prime \prime } ( x ) d x = 40$, then the correct expression(s) is(are)
(A) $9 f ^ { \prime } ( 3 ) + f ^ { \prime } ( 1 ) - 32 = 0$
(B) $\int _ { 1 } ^ { 3 } f ( x ) d x = 12$
(C) $9 f ^ { \prime } ( 3 ) - f ^ { \prime } ( 1 ) + 32 = 0$
(D) $\int _ { 1 } ^ { 3 } f ( x ) d x = - 12$

If $\int _ { 1 } ^ { 3 } x ^ { 2 } F ^ { \prime \prime } ( x ) d x = - 12$ and $\int _ { 1 } ^ { 3 } x ^ { 3 } F ^ { \prime \prime } ( x ) d x = 40$, then the correct expression(s) is(are)\\
(A) $9 f ^ { \prime } ( 3 ) + f ^ { \prime } ( 1 ) - 32 = 0$\\
(B) $\int _ { 1 } ^ { 3 } f ( x ) d x = 12$\\
(C) $9 f ^ { \prime } ( 3 ) - f ^ { \prime } ( 1 ) + 32 = 0$\\
(D) $\int _ { 1 } ^ { 3 } f ( x ) d x = - 12$

Paper Questions

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