Integration of (x+1 x ) with respect to x : - Vidyadip

MCQ

Integration of $\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)$ with respect to $x$ :

A
$\frac{1}{3} x^{\frac{1}{3}}+2 x^{\frac{1}{2}}+ C$
B
$\frac{2}{3} x^{\frac{2}{3}}+\frac{1}{2} x^2+ C$
✓
$\frac{2}{3} x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+ C$
D
$\frac{3}{2} x^{\frac{3}{2}}+\frac{1}{2} x^{\frac{1}{2}}+ C$

✓

Answer

Correct option: C.

$\frac{2}{3} x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+ C$

(C)
Let $I =\int\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right) d x$
$
\begin{array}{l}
=\int\left(x^{\frac{1}{2}}+x^{-\frac{1}{2}}\right) d x \\
=\frac{x^{\frac{3}{2}}}{\frac{3}{2}}+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+C
\end{array}
$
$
=\frac{2}{3} x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+C
$
Hence correct option is (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 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 in a $\triangle\text{ABC}$, $\text{A}=(0,0),\ \text{B}=(3,3\sqrt3),\ \text{C}=(-3\sqrt3,3)$, then the vecctor of magnitude $2\sqrt2$ units directed along AO, where O is the circumcenter of $\triangle\text{ABC}$ is,

$(1-\sqrt3)\hat{\text{i}}+(1+\sqrt3)\hat{\text{j}}$
$(1+\sqrt3)\hat{\text{i}}+(1-\sqrt3)\hat{\text{j}}$
$(1+\sqrt3)\hat{\text{i}}+(\sqrt3-1)\hat{\text{j}}$
None of these

${x_1} + 2{x_2} + 3{x_3} = a2{x_1} + 3{x_2} + {x_3} = $ $b3{x_1} + {x_2} + 2{x_3} = c$ this system of equations has

Let $y=y(x)$ be the solution of the differential equation

$x \tan \left(\frac{y}{x}\right) d y=\left(y \tan \left(\frac{y}{x}\right)-x\right) d x,-1 \leq x \leq 1, y\left(\frac{1}{2}\right)=\frac{\pi}{6}$

Then the area of the region bounded by the curves $x=0, x=\frac{1}{\sqrt{2}}$ and $y=y(x)$ in the upper half plane is :

For $\alpha, \beta \in \mathrm{R}$ and a natural number $\mathrm{n}$, let

$A_r=\left|\begin{array}{ccc}r & 1 & \frac{n^2}{2}+\alpha \\ 2 r & 2 & n^2-\beta \\ 3 r-2 & 3 & \frac{n(3 n-1)}{2}\end{array}\right|$. Then $2 A_{10}-A_8$

The number of commutative binary operation that can be defined on a set of 2 elements is:

8
6
4
2

The area of the ellipse $\frac{\text{x}2}{9}+\frac{\text{y}^2}{4}=1$ in first quadrant is $6\pi$ sq. units.
The ellipse is rotated about its centre in anti-clockwise direction till its major axis coincides with y-axis. Now the area of the ellipse in first Quadrant is $\pi$ sq. units.

2
4
6
8

Choose the correct answer from the given four options.
A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is:

Given vectors $a, b, c $ such that $a\,.(b \times c)$$ = \lambda \ne 0,\,$ the value of $(b \times c)\,.\,(a + b + c)/\lambda $ is

The solution of the equation $\frac{{dy}}{{dx}} = \frac{{x + y}}{{x - y}}$ is

A rectangular parallelopiped is formed by planes drawn through the point (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is:

2
3
4
all of these