Evaluate : 2 x 5 x 3 x d x - Vidyadip

Question

Evaluate : $\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} \ d x$

✓

Answer

Let $I =\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} \ d x$.
Then, we have
$I=\int \frac{\sin (5 x-3 x)}{\sin 5 x \sin 3 x} \ d x$
$=\int \frac{\sin 5 x \cos 3 x-\cos 5 x \sin 3 x}{\sin 5 x \sin 3 x}\ d x$
$=\int \frac{\sin 5 x \cos 3 x}{\sin 5 x \sin 3 x} d x-\int \frac{\cos 5 x \sin 3 x}{\sin 5 x \sin 3 x} d x$
$=\int \frac{\cos 3 x}{\sin 3 x} d x-\int \frac{\cos 5 x}{\sin 5 x}\ d x$
$=\int \cot 3 x d x-\int \cot 5 x\ d x$
$=\frac{1}{3} \log |\sin 3 x|-\frac{1}{5} \log |\sin 5 x|+c$
$\therefore I=\frac{1}{3} \log |\sin 3 x|-\frac{1}{5} \log |\sin 5 x|+c$

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 Model Paper 9→Model Paper 9 — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write the coordinates of the projection of point P(x, y, z) on XOZ-plane.

Give an example of a relation which is,Reflexive and transitive but not symmetric.

Write the projection of $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ along the vector $\hat{\text{j}}.$

Evaluate the following definite integrals:
$\int_{0}^\limits{\frac{\pi}{2}}\text{x}^2\cos\text{x}\text{ dx}$

Find the area of the region bounded by $y=|x|$, $x =-3, x =1$ and the $x-$ axis.

Write the value of $\cos^{-1}(\cos1540^\circ).$

Find the value of the determinant $\begin{vmatrix}243&156&300\\81&52&100\\-3&0&4\end{vmatrix}$

For a positive constant a find $\frac{{dy}}{{dx}}$, wherer $y = {a^{\left( {t + \frac{1}{t}} \right)}}$ and $x = {\left( {t + \frac{1}{t}} \right)^a}$.

Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal's selection is $\frac{1}{3}$ and that of Monika's selection is $\frac{1}{5}$. Find the probability that.
Both of them will be selected.

If y = x|x|, find $\frac{\text{dy}}{\text{dx}}\text{ for x 0}<0.$