_ ^ a^x ;da = - Vidyadip

MCQ

$\int_{}^{} {{a^x}\;da = } $

A
$\frac{{{a^x}}}{{{{\log }_e}a}} + c$
B
${a^x}{\log _e}a + c$
✓
$\frac{{{a^{x + 1}}}}{{x + 1}} + c$
D
$x{a^{x - 1}} + c$

✓

Answer

Correct option: C.

$\frac{{{a^{x + 1}}}}{{x + 1}} + c$

c
(c)$\int_{}^{} {{a^x}da} = \frac{{{a^{x + 1}}}}{{x + 1}} + c.$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\alpha $ and $\beta $ are different complex numbers with $|\beta | = 1$, then $\left| {\frac{{\beta - \alpha }}{{1 - \overline \alpha \beta }}} \right|$ is equal to

$\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\{{{(a + 1)}^2}}&{{{(b + 1)}^2}}&{{{(c + 1)}^2}}\\{{{(a - 1)}^2}}&{{{(b - 1)}^2}}&{{{(c - 1)}^2}}\end{array}\,} \right| = $

Let $A_{1}, A_{2}, A_{3}, \ldots \ldots . .$ be squares such that for each $n \geq 1,$ the length of the side of $A _{ n }$ equals the length of diagonal of $A _{ n +1}$. If the length of $A _{1}$ is $12\, cm ,$ then the smallest value of $n$ for which area of $A _{ n }$ is less than one, is ..........

If $\,\,f(x) = \left\{ {\begin{array}{*{20}{c}}
{3 + x;\,\,\,\,\,x \geqslant 0} \\
{2 - 3x;\,\,\,\,\,x < 0}
\end{array}} \right.$ then $\mathop {\lim }\limits_{x \to 0} f(f(x))$ is equal to -

The number of distinct real roots of the equation $x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0$ is

Consider a branch of the hyperbola $x^2-2 y^2-2 \sqrt{2} x-4 \sqrt{2} y-6=0$ with vertex at the point $A$. Let $B$ be one of the end points of its latus rectum. If $\mathrm{C}$ is the focus of the hyperbola nearest to the point $\mathrm{A}$, then the area of the triangle $\mathrm{ABC}$ is

If $3^{2 \sin 2 \alpha-1},14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an $A.P.$ for some $\alpha$, then the sixth term of this $A.P.$ is

The number of ways in which first, second and third prizes can be given to $5$ competitors is

A straight line through $P(1, 2)$ is such that its intercept between the axes is bisected at $P$ Its equation is

A particle moves in a straight line in such a way that its velocity at any point is given by ${v^2} = 2 - 3x$, where $x$ is measured from a fixed point. The acceleration is