Integrate the function: x 1 + x - Vidyadip

Question

Integrate the function: $\frac{{\sin x}}{{1 + \cos x}}$

✓

Answer

Let $I = \int {\frac{{\sin x}}{{1 + \cos x}}dx} $

$= - \int {\frac{{ - \sin x}}{{1 + \cos x}}dx} $ ...(i)

Putting 1 + cos x = t

$\Rightarrow - \sin x = \frac{{dt}}{{dx}}$

$\Rightarrow - \sin xdx = dt$

$\therefore$ From eq. (i), $I = - \int {\frac{{dt}}{t}}$

= - log |t| + c

= -log |1 + cos 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 Integrals→Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Prove the points $(a, b+c),(b, c+a),(c, a+b)$ are collinear.

Find equation of line joining (1, 2) and (3, 6) using determinants.

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

Find the maximum value of $2{x^3} - 24x + 107$ in the interval [1, 3]. Find the maximum value of the same function in $\left[ { - 3, - 1} \right]$

If $A$ is a square matrix, then write the matrix adj $(A^T) − ($adj $A)^T.$

If X denotesthe number on the uper face of a cubical die when it is thrown, find the mean of X.

If $A$ is $2\times 3$ matrix and $B$ is a matrix such that $A^T B$ and $BA^T$ both are defined, then what is the order of $B?$

If $A = \{a, b, c, d\}$ and the function $f = \{(a, b), (b, d), (c, a), (d, c)\},$ write $f^{-1}.$

Find the absolute maximum value and the absolute minimum value of the function:
f(x) = sin x + cos x , x $\in$ [0, $\pi$]

Write the number of all possible matrices of order $2\times 2$ with each entry $1, 2$ or $3.$