x+2 dx - Vidyadip

Question

$\int\text{x}\sqrt{\text{x}+2}\ \text{dx}$

✓

Answer

Let I $=\int\text{x}\sqrt{\text{x}+2}\text{ dx}.$ Then,
$\text{I}=\int\{(\text{x}+2)-2\}\text{x}+2\text{dx}\ \ \ [\because\text{x}=(\text{x}+2)-2]$
$\Rightarrow\text{I}=\int\Big\{(\text{x}+2)^\frac{3}{2}-2(\text{x}+2)^\frac{1}{2}\Big\}\text{dx}$
$\Rightarrow\text{I}=\frac{2}{5}(\text{x}+2)^\frac{5}{2}-\frac{4}{3}(\text{x}+2)^\frac{3}{2}+\text{C}$

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 "4 Marks" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Verify Rolle's theorem for the following function on the indicated intervals

$\text{f}(\text{x})=\sin2\text{x}\text{ on }\Big[0,\frac{\pi}{2}\Big]$

Let $\text{A}=\begin{bmatrix}3 & 2 \\7 & 5 \end{bmatrix}\text{and B}=\begin{bmatrix}6 & 7 \\8 & 9 \end{bmatrix}$. Find (AB)^-1.

If possible, find BA and AB, where $\text{A}=\begin{bmatrix}2&1&2\\1&2&4\end{bmatrix}$ and $\text{B}=\begin{bmatrix}4&1\\2&3\\1&2\end{bmatrix}.$

If $\text{y}=\frac{1}{2}\log\Big(\frac{1-\cos2\text{x}}{1+\cos2\text{x}}\Big),$ Prvoe that $\frac{\text{dy}}{\text{dx}}=2\text{ cosec }2\text{x}$

For the following matrices verify the distributivity of matrix, multiplication over matrix addtion i.e., A(B + C) = AB + AC.
$\text{A}=\begin{bmatrix}2&-1\\1&1\\-1&2\end{bmatrix},\text{B}=\begin{bmatrix}0&1\\1&1\end{bmatrix}$ and $\text{C}=\begin{bmatrix}1&-1\\0&1\end{bmatrix}$

The function $\text{f(x)}=\begin{cases}\frac{\text{x}^2}{\text{a}},&\text{if }0\leq\text{ x}<1\\\text{a},&\text{if }1\leq\text{x}<\sqrt{2}\\\frac{2\text{b}^2-4\text{b}}{\text{x}^2},&\text{if }\sqrt{2}\leq\text{x}<\infty\end{cases}$ is continuous on $(0,\infty),$ then find the most suitable value of a and b.

Evaluate the following integrals:
$\int(\text{x}+1)\sqrt{\text{x}^2+\text{x}+1}\text{dx}$

Without expanding, show that the values of the following determinant are zero:
$\begin{vmatrix}1^2&2^2&3^2&4^2\\2^2&3^2&4^2&5^2\\3^2&4^2&5^2&6^2\\4^2&5^2&6^2&7^2\end{vmatrix}$

Using integration, find the area of the region enclosed by the parabola y = 3x² and the line 3x - y + 6 = 0.

Evaluate the following integrals as limit of sum:
$\int\limits^2_{1}\text{x}^2\text{ dx}$