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

Find the shortest distance between the lines $\frac{\text{x}+1}{7}=\frac{\text{y}+1}{-6}=\frac{\text{z}+1}{0}$ and $\frac{\text{x}-3}{1}=\frac{\text{y}-5}{-2}=\frac{\text{z}-7}{1}.$

Kellogg is a new cereal formed of a mixture of bran and rice that contains at least 88 grams of protein and at least 36 milligrams of iron. Knowing that bran contains 80 grams of protein and 40 milligrams of iron per kilogram, and that rice contains 100 grams of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs. 5 per kg and rice costs Rs 4 per kg.

Evaluate the following definite integrals:
$\int\limits_{\frac{\pi}{2}}^{\pi}\text{e}^{\text{x}}\Big(\frac{1-\sin\text{x}}{1-\cos\text{x}}\Big)\text{dx}$

If $x, y, z \in[-1,1]$ such that $\sin ^{-1} x+\sin ^{-1} y+$ $\sin ^{-1} z=\frac{-3 \pi}{2}$ then find the value of $x^2+y^2+z^2$.

A company manufactures two articles A and B. There are two departments through which these articles are processed: (i) assembly and (ii) finishing departments. The maximum capacity of the first department is 60 hours a week and that of other department is 48 hours per week. The product of each unit of article A requires 4 hours in assembly and 2 hours in finishing and that of each unit of B requires 2 hours in assembly and 4 hours in finishing. If the profit is Rs. 6 for each unit of A and Rs 8 for each unit of B, find the number of units of A and B to be produced per week in order to have maximum profit.

If $\tan(\text{x}+\text{y})+\tan(\text{x}+\text{y})=1,$ find $\frac{\text{dy}}{\text{dx}}$

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

If $\text{A}=\begin{bmatrix}2&-1\\3&2 \end{bmatrix} $ and $\text{B}=\begin{bmatrix}0&4\\-1&7\end{bmatrix} ,$ find 3A² - 2B + l

Let Z be the set of all integers and Z₀ be the set of all non-zero integers. Let a relation R on Z × Z₀ be defined as (a, b)R(c, d) ⇔ ad = bc for all (a, b), (c, d) ∈ Z × Z₀, Prove that R is an equivalence relation on Z × Z₀.

Find the value of $\lambda$ for which the four points with position vectors
$-\hat{\text{j}}-\hat{\text{k}},4\hat{\text{i}}+5\hat{\text{j}}+\lambda\hat{\text{k}},3\hat{\text{i}}+9\hat{\text{j}}+4\hat{\text{k}}$ and $-4\hat{\text{i}}+4\hat{\text{j}}+4\hat{\text{k}}$ are co planar.