bac-s-maths 2022 Q5

bac-s-maths · France · bac-spe-maths__metropole-sept_j1 Integration by Parts Multiple-Choice Primitive Identification

Let $f$ be the function defined on $] 0 ; + \infty \left[ \text{ by } f ( x ) = x ^ { 2 } \ln x \right.$.
A primitive $F$ of $f$ on $] 0$; $+ \infty [$ is defined by: a. $F ( x ) = \frac { 1 } { 3 } x ^ { 3 } \left( \ln x - \frac { 1 } { 3 } \right)$; b. $F ( x ) = \frac { 1 } { 3 } x ^ { 3 } ( \ln x - 1 )$; c. $F ( x ) = \frac { 1 } { 3 } x ^ { 2 }$; d. $F ( x ) = \frac { 1 } { 3 } x ^ { 2 } ( \ln x - 1 )$.

Let $f$ be the function defined on $] 0 ; + \infty \left[ \text{ by } f ( x ) = x ^ { 2 } \ln x \right.$.

A primitive $F$ of $f$ on $] 0$; $+ \infty [$ is defined by:\\
a. $F ( x ) = \frac { 1 } { 3 } x ^ { 3 } \left( \ln x - \frac { 1 } { 3 } \right)$;\\
b. $F ( x ) = \frac { 1 } { 3 } x ^ { 3 } ( \ln x - 1 )$;\\
c. $F ( x ) = \frac { 1 } { 3 } x ^ { 2 }$;\\
d. $F ( x ) = \frac { 1 } { 3 } x ^ { 2 } ( \ln x - 1 )$.

Paper Questions

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