Evaluate: (x - ) (x + ) dx - Vidyadip

Question

Evaluate:

$\int \frac{\sin (\text{x} - \alpha)}{\sin (\text{x} + \alpha)} \text{dx}$

✓

Answer

$I = \int \frac{\sin(x + a)-2\alpha)}{\sin(x + \alpha)}$

$= \int \frac{\sin(x + \alpha). \cos 2\alpha - \cos (x + \alpha) .2 \alpha}{\sin(x + \alpha)} dx$

$= \cos 2 \alpha \int dx - \sin 2 \alpha \int \frac{\cos(x + \alpha)}{\sin(x + \alpha)} dx$

$= x \cos 2 \alpha - \sin 2 \alpha \log |\sin (x + \alpha)|+c$

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 "3 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

Let O be the origin. We define a relation between two points P and Q in a plane if OP = OQ. Show that the relation, so defined is an equivalence relation.

Let S be a relation on the set R of all real numbers defined by S = {(a, b) ∈ R × R: a² + b² = 1} prove that S is not an equivalence relation on R.

ABCDE is a pentagon, prove that,

$\overrightarrow{\text{AB}}+\overrightarrow{\text{AE}}+\overrightarrow{\text{BC}}+\overrightarrow{\text{DC}}+\overrightarrow{\text{ED}}+\overrightarrow{\text{AC}}=3\ \overrightarrow{\text{AC}}$

Find the distance of the point P(-1, -5, -10) from the point of intersection of the line joining the points A(2, -1, 2) and B(5, 3, 4) with the plane x - y + z = 5.

Evaluate the following integrals:
$\int5^{\text{x}+\tan^{-1}\text{x}}.\Big(\frac{\text{x}^2+2}{\text{x}^2+1}\Big)\text{dx}$

The radius of a circle is increasing at the rate of 0.7cm/ sec. What is the rate of increase of its circumfrence?

If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is $\sqrt{3.}$

Find a unit vector perpendicular to both the vectors $4\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$ and $-2\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}.}$

If $\text{A}=\begin{bmatrix}2&-3&-5\\-1&4&5\\1&-3&-4\end{bmatrix},$ show that A² = A.

If the vertices A, B, C of a triangle ABC are the points with position vectors $\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}},\ \text{b}_1\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}},\ \text{c}_1\hat{\text{i}}+\text{c}_2\hat{\text{j}}+\text{c}_3\hat{\text{k}}$ respectively, what are the vectors determined by its sides? Find the length of these vectors.