If a^x e^ 2x b^x c^x dx = 1 k ( a^x e^ 2x b^x c^x ) + l then k = - Vidyadip

MCQ

If $\int {\frac{{{a^x}{e^{2x}}}}{{{b^x}{c^x}}}dx = \frac{1}{k}\left( {\frac{{{a^x}{e^{2x}}}}{{{b^x}{c^x}}}} \right)} + l$ then $k =$

A
$log\, b + log \,c -log\, a -2$
B
$log\, (e^2 \,abc)$
✓
$log\, a -log\, b -log\, c + 2$
D
$2\, log\, a + log\, b -log\, c$

✓

Answer

Correct option: C.

$log\, a -log\, b -log\, c + 2$

c
$\int\left(\frac{\mathrm{ae}^{2}}{\mathrm{bc}}\right)^{\mathrm{x}} \mathrm{dx}$

$\frac{{{{\left( {\frac{{{\rm{a}}{{\rm{e}}^2}}}{{{\rm{bc}}}}} \right)}^{\rm{x}}}}}{{\ln \frac{{{\rm{a}}{{\rm{e}}^2}}}{{{\rm{bc}}}}}} + l$

$\therefore {\rm{k}} = \ln \frac{{{\rm{a}}{{\rm{e}}^2}}}{{{\rm{bc}}}}$

$ = \ln {\rm{a}} + 2 - \ln {\rm{b}} - \ln {\rm{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

More "M.C.Q (1 Marks)" from 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\mathrm{A}=\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right],$ then verify that $\mathrm{A}$ $\mathrm{adj}$ $\mathrm{A}=| \mathrm{A} | \mathrm{I}$. Also find $\mathrm{A}^{-1}$.

Let $f : R \rightarrow R$ be continuous function satisfying $f ( x )+ f ( x + k )= n$, for all $x \in R$ where $k >0$ and $n$is a positive integer. If $I _{1}=\int\limits_{0}^{4 n k} f ( x ) dx$ and $I _{2}=\int\limits_{- k }^{3 k } f ( x ) dx$, then

Let $y=y(x)$ be the solution of the differential equation $\begin{array}{l} \cos x(3 \sin x+\cos x+3) d y= (1+y \sin x(3 \sin x+\cos x+3)) d x \end{array}$ ; $0 \leq x \leq \frac{\pi}{2}, y(0)=0 .$ Then $, y\left(\frac{\pi}{3}\right)$ is equal to ..... .

Let $P$ be a non-zero polynomial such that $P(1+x)=P(1-x)$ for all real $x$ and $P(1)=0$. Let $m$ be the largest integer such that $(x-1)^m$ divides $P(x)$ for all such $P(x)$. Then, $m$ equals

Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|\mathrm{A}| \neq 0 .$ Consider the following two statements :

$(P)$ If $A \neq I_{2},$ then $|A|=-1$

$(\mathrm{Q})$ If $|\mathrm{A}|=1,$ then $\operatorname{tr}(\mathrm{A})=2$

where $I_{2}$ denotes $2 \times 2$ identity matrix and $\operatorname{tr}(A)$ denotes the sum of the diagonal entries of $A$ Then

$\mathop {Limit}\limits_{n\,\, \to \,\,\infty } \, \frac{1}{n}\,\,\,\left[ {\,1\,\, + \,\,\sqrt {\frac{n}{{n\,\, + \,\,1}}} \,\,\, + \,\,\,\sqrt {\frac{n}{{n\,\, + \,\,2}}} \,\,\, + \,\,\,\sqrt {\frac{n}{{n\,\, + \,\,3}}} \,\,\, + \,\,\,.......\,\,\, + \,\,\,\sqrt {\frac{n}{{n\,\, + \,\,3\,\,(n\,\, - \,\,1)}}} \,} \right]$ has the value equal to

The relation $R =\{(a, b),(b, a)\}$ is defined on the set $\{a, b, c\}$, then R is ____________ .

If ${a_{1,}}{a_2},{a_3}.....,{a_n}$ is an $A.P.$ with common difference d then $\tan \left[ {{{\tan }^{ - 1}}\left( {\frac{d}{{1 + {a_1}{a_2}}}} \right) + {{\tan }^{ - 1}}\left( {\frac{d}{{1 + {a_2}{a_3}}}} \right) + ...} \right.$ $\left. { + {{\tan }^{ - 1}}\left( {\frac{d}{{1 + {a_{n - 1}}{a_n}}}} \right)} \right] = $

If $p + q + r = 0 = a + b + c$, then the value of the determinant $\left| {\,\begin{array}{*{20}{c}}{pa}&{qb}&{rc}\\{qc}&{ra}&{pb}\\{rb}&{pc}&{qa}\end{array}\,} \right|$ is

The domain of function $\sin ^{-1} 2 x$ is :