_ ^ dx x + a + x + b = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{\sqrt {x + a} + \sqrt {x + b} }}} = $

A
$\frac{2}{{3(b - a)}}[{(x + a)^{3/2}} - {(x + b)^{3/2}}] + c$
✓
$\frac{2}{{3(a - b)}}[{(x + a)^{3/2}} - {(x + b)^{3/2}}] + c$
C
$\frac{2}{{3(a - b)}}[{(x + a)^{3/2}} + {(x + b)^{3/2}}] + c$
D
None of these

✓

Answer

Correct option: B.

$\frac{2}{{3(a - b)}}[{(x + a)^{3/2}} - {(x + b)^{3/2}}] + c$

b
(b)$\int_{}^{} {\frac{{dx}}{{\sqrt {x + a} + \sqrt {x + b} }} = \int_{}^{} {\frac{{\sqrt {x + a} - \sqrt {x + b} }}{{(x + a) - (x + b)}}\,dx} } $

$ = \frac{1}{{(a - b)}}\int_{}^{} {{{(x + a)}^{1/2}}dx} - \frac{1}{{(a - b)}}\int_{}^{} {{{(x + b)}^{1/2}}dx} $

$[ = \frac{2}{{3(a - b)}}[{(x + a)^{3/2}} - {(x + b)^{3/2}}] + c.]$

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

Let the set of all positive values of $\lambda$, for which the point of local minimum of the function $\left(1+x\left(\lambda^2-x^2\right)\right)$ satisfies $\frac{x^2+x+2}{x^2+5 x+6}<0$, be $(\alpha, \beta)$. Then $\alpha^2+\beta^2$ is equal to........

For $k \in R$, let the solutions of the equation $\cos \left(\sin ^{-1}\left(x \cot \left(\tan ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)\right)\right)\right)=k, 0\,<\,|x|<\,\frac{1}{\sqrt{2}}$ be $\alpha$ and $\beta$, where the inverse trigonometric functions take only principal values. If the solutions of the equation $x ^{2}- bx -5=0$ are $\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}$ and $\frac{\alpha}{\beta}$, then $\frac{b}{k^{2}}$ is equal to$......$

Which of the following sets are convex?

$\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\geq1\}$
$\{(\text{x},\text{y}):\text{y}^2\geq\text{x}\}$
$\{(\text{x},\text{y}):3\text{x}^2+4\text{y}^2\geq5\}$
$\{(\text{x},\text{y}):\text{y}\geq2,\text{y}\leq4\}$

An integer $x$ is chosen at random from $1$ to $50$ . The probability that $x +\frac{336}{x} \leq 50 $ is

The area (in sq. units) of the region $A=\{(x, y):(x-1)[x] \leq y \leq 2 \sqrt{x}, 0 \leq x \leq 2\}$ where $[t]$ denotes the greatest integer function, is

Let the function $\mathrm{g}:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $g(\mathrm{u})=2 \tan ^{-1}\left(e^{\mathrm{u}}\right)-\frac{\pi}{2}$. Then, $\mathrm{g}$ is

The general solution of differention eqution of the e^x dy + (ye^x + 2x)dx = 0 is:

xe^y + x²= C
xe^y+ y²= C
ye^x + y²= C
ye^y+ x² = C

Choose the correct answer from the given four options.
Let us define a relation R in R as aRb if a ≥ b. Then R is:

An equivalence relation.
Reflexive, transitive but not symmetric.
Symmetric, transitive but not reflexive.
Neither transitive nor reflexive but symmetric.

Four forces act on a point object. The object will be in equilibrium, if:

All of them are in the same plane
They are opposite to each other in pairs
The sum of x, y and z-components of forces zero separately
They form a closed figure of 4 sides when added as Polygon law

The value of $\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\big(\text{x}^3+\text{x}\cos\text{x}+\tan^5\text{x}+1\big)\text{dx},$ is:

0
2
$\pi$
1