Find the integral: (2 x^ 2 -3 x+5 x ) d x - Vidyadip

Question

Find the integral: $\int\left(2 x^{2}-3 \sin x+5 \sqrt{x}\right) d x$

✓

Answer

$\int\left(2 x^{2}-3 \sin x+5 \sqrt{x}\right) d x$
= $2 \int x^{2} d x-3 \int \sin x d x+5 \int x^{\frac{1}{2}} d x$
= $\frac{2 x^{3}}{3}+3 \cos x+5\left(\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right)+C$
= $\frac{2 x^{3}}{3}+3 \cos x+\frac{10}{3} x^{\frac{3}{2}}+C$

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 Questions" 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 formula for the shortest distance between the lines$\vec{\text{r}}=\vec{\text{a}}_1+\lambda\vec{\text{b}}$ and $\vec{\text{r}}=\vec{\text{a}}_2+\mu\vec{\text{b}}.$

If $A = [a_{ij}]$ is a $2 \times 2$ matrix such that $a_{ij} = i + 2j$, write $A$.

Find $\int \frac{\text{d}x}{x^{2} + 4x + 8}$

Evaluate the following integrals:
$\int\text{x}^{\frac{5}{4}}\text{dx}$

If a line makes angles 90º, 135º, 45º with the x, y and z-axes respectively, find its direction cosines.

Find the values:
$\cot\left(\tan^{-1}a+\cot^{-1}a\right)$

Evaluate the following integrals:
$\int\frac{1}{3\sqrt{\text{x}^2}}\text{dx}$

If A is an invertible matrix such that $|A^{-1}| = 2$, find the value of $|A|$.

If $y=\tan ^{-1}\left(\frac{2^{x+1}}{1-4^x}\right)$ then find $\frac{d y}{d x}$.

Find the second order derivatives of the function given in Exercise:
$\sin(\log\text{x})$