Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
If $\text{g}'(\text{x})=\int\text{x}^\text{x}\log_\text{e}(\text{ex})\text{dx}$ then $\text{g}(\pi)$ equals :
  • A
    $\pi\log_\text{e}\pi$
  • B
    $\pi^\pi\log_\text{e}(\text{e}\pi)$
  • C
    $\pi^\pi\log_\text{e}(\pi)$
  • ✓
    $\pi^\pi$
✓

Answer

Correct option: D.
$\pi^\pi$
$\text{g}\ '(\text{x})=\int\text{x}^{\text{x}}(1+\log{\text{e}^\text{x}})\text{dx}$
$=\int\text{d}(\text{x}^{\text{x}})$
$\text{g'}(\text{x})=\text{x}^{\text{x}}$
$\text{g'}({\pi})={\pi}^{\pi}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $A$ is square matrix of order 3 , then $\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|=$
→
If $\text{A}=\begin{bmatrix}1&\text{a}\\0&1\end{bmatrix},$ then $A^n\ ($where $n \in N$) equals :
→
$\int\frac{1}{1+\tan\text{x}}\text{ dx}=$
→
India play two matches each with West indies and Australia. In any match the probability of india getting $0,1$ and $2$ points are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are indepecdent, the probability of india getting at least $7$ points is.
→
If a function $g(x)$ is defined in $[-1, 1]$ and two vertices of an equilateral triangle are $(0, 0)$ and $(x, g(x))$ and its area is $\frac{\sqrt 3}{4}$ , then $g(x)$ equals :-
→
In each of the following choose the correct answer:If A and B are events such that $\text{P}(\text{A}|\text{B})=\text{P}(\text{B}|\text{A}),\ \text{then}:$
→
If $ab = 2a + 3b,\,a > 0,\,\,b > 0$ then the minimum value of  $ ab$  is
→
If $A$ and $B$ are independent events such that $P ( A )=\frac{1}{5}, P ( A \cup B )=\frac{7}{10}$, then what is $P (\bar{B})$ equal to?
→
If $x$ is parallel to $y$ and $z$ where $x = 2i + j + \alpha k$, $y = \alpha i + k$ and $z = 5i - j$, then $\alpha $ is equal to
→
The area of the circle $x^2+ y^2 = 16$ enterior to the parabola $y^2 = 6x$ is :
→