Integrate the function: x 1+2 x^ 2 - Vidyadip

Question

Integrate the function: $x \sqrt{1+2 x^{2}}$

✓

Answer

Let 1 + 2x² = t
$\Rightarrow$ 4xdx = dt
$\Rightarrow\int x \sqrt{1+2 x^{2}} d x=\int \frac{\sqrt{t} d t}{4}$
$\Rightarrow\frac{1}{4} \int t^{\frac{1}{2}} d t$
$\Rightarrow \frac{1}{4}\left(\frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right)+C$
$\Rightarrow \frac{1}{6}\left(1+2 x^{2}\right)^{\frac{3}{2}}+C$

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 "2 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

Write the value of $\tan^{-1}\sqrt3+\cot^{-1}\sqrt3$

Write the intercept cut off by the plane 2x + y − z = 5 on x-axis.

Find the value of x for which $\text{x}\Big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\Big)$ is a unit vector.

For any square matrix write whether AA^T is symmetric or skew-symmetric.

Let 'o' be a binary operation on the set Q₀ of all non-zero rational numbers defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2} $ for all $\text{a},\text{b}\in\text{Q}_0.$
Find the identity element in Q₀.

If f(x) = 4 - (x - 7)³, then write f^-1(x).

A random variable X has the following probability distribution:

Values of X:	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	k

Find the value of k.

Find the values of $k$ so that the function $f$ is continuous at $x=\frac{\pi}{2}$
$f(x)=\left\{\begin{array}{cc}
\frac{k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\
3, & x=\frac{\pi}{2}
\end{array}\right.$

Define identity element for a binary operation defined on a set.

Let $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix}$ and $\text{C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}.$ Find each of the following:
$3\text{A}-2\text{B}+3\text{C}$