MCQ
$\int\limits_2^3 {\frac{{{{(x + 2)}^2}}}{{2{x^2} - 10x + 53}}} dx = $
  • A
    $2$
  • B
    $1$
  • $\frac{1}{2}$
  • D
    $\frac{5}{2}$

Answer

Correct option: C.
$\frac{1}{2}$
c
$\int_{a}^{b} \frac{f(x)}{f(a+b-x)+f(x)} d x=\frac{b-a}{2}$

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

Similar questions

A ship is fitted with three engines $E_1, E_2$ and $E_3$. The engines function independently of each other with respective probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$. For the ship to be operational at least two of its engines must function. Let $X$ denote the event that the ship is operational and let $X _1, X _2$ and $X _3$ denotes respectively the events that the engines $E_1 E_2$ and $E_3$ are functioning. Which of the following is (are) true?

$(A)$ $P\left[X_1^c \mid x\right]=\frac{3}{16}$

$(B)$ $P [$ Exactly two engines of the ship are functioning $\mid X ]=\frac{7}{8}$

$(C)$ $P\left[X \mid X_2\right]=\frac{5}{16}$

$(D)$ $P\left[X \mid X_1\right]=\frac{7}{16}$

Let f : R → R be a function defined by $\text{f(x)}=\frac{\text{e}^{|\text{x}|}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}.$ Then,
  1. f is a bijection.
  2. f is an injection only.
  3. f is surjection on only.
  4. f is neither an injection nor a surjection.
Difference between sample space and subset of sample space is considered as:
  1. Numerical complementary events.
  2. Equal compulsory events.
  3. Complementary events.
  4. Compulsory events.
Derivative of $e^{2 x}$ with respect to $e^x$, is
Region represented by $\text{x}\geq0, \text{y}\geq0$ is:
Find the values of $k$ so that the function $f$ is continuous at the indicated point.

$f(x) = \left\{ {\begin{array}{*{20}{l}}
{\frac{{k\cos x}}{{\pi  - 2x}},}&{{\rm{ if }}\,x\, \ne \,\frac{\pi }{2}}\\
{3,}&{{\rm{ if }}\,x\, = \,\frac{\pi }{2}}
\end{array}} \right.$    at $x = \frac{\pi }{2}$

If $y = \sqrt {\log x + \sqrt {\log x + \sqrt {\log x + .....\infty } } } $, then ${{dy} \over {dx}} = $
If the fucnction $\text{f(x)}=\begin{cases}(\cos\text{x})^{\frac{1}{\text{x}}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuouse at x = 0, then the value of k is:
  1. 0
  2. 1
  3. -1
  4. e
The derivative of $F[f\{ \phi (x)\} ]$ is
Let $\mathrm{f}(\mathrm{x})=\cos \left(2 \tan ^{-1} \sin \left(\cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{\mathrm{x}}}\right)\right)$ $0<\mathrm{x}<1$. Then :