Integrate the functions in Exercises: - Vidyadip

Question

Integrate the functions in Exercises:
$\cot\text{x}\log\sin\text{x}$

✓

Answer

$\text{Let I}=\int\cot\text{x }\log\sin\text{x}\text{ dx} \ \ \ \ \ \ \ ...\text{(i)} $
Putting $\log\sin\text{x}=\text{t}\ \ \ \Rightarrow\ \ \ \frac{1}{\sin\text{x}}\frac{\text{d}}{\text{dx}}(\sin\text{x})=\frac{\text{dt}}{\text{dx}}\ \ \ \Rightarrow \ \ \ \frac{1}{\sin\text{x}}\cos\text{x}=\frac{\text{dt}}{\text{dx}} $
$\Rightarrow\ \ \ \cot\text{ x dx = dt} $
$\therefore\ \ \ \ $From eq. (i), $\text{I}=\int\text{t dt}=\frac{\text{t}^2}{2}+\text{c}=\frac{1}{2}(\log \sin\text{x})^2+\text{c}$

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 "1 Marks Question" 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

Find the sum of the order and degree of the differential equation $\text{y}=\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{3}+\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}.$

Find the principal value of the following:
$\sin^{-1}\Big(\tan\frac{5\pi}{4}\Big)$

Find the maximum and the minimum values, if any, of the function given by $f(x) = x, x \in (0, 1)$.

Evaluate the following integrals:
$\int\log_\text{x}\text{xdx}$

If matrix $A+B=\left[\begin{array}{ll}2 & 4 \\ 1 & 2\end{array}\right], A-B=\left[\begin{array}{ll}0 & 1 \\ 2 & 2\end{array}\right]$, then find matrix $A$.

Integrate the functions in Exercises:
$\frac{\text{e}^{2\text{x}}-\text{e}^{-2\text{x}}}{\text{e}^{2\text{x}}+\text{e}^{-2\text{x}}}$

One card is drawn at random from a well shuffled deck of 52 cards.
In which of the following cases are the events E and F independent?
E: the card drawn is a spade
F: the card drawn is an ace

Find values of x, if:
$\begin{vmatrix}2&3\\4&5\end{vmatrix}=\begin{vmatrix}\text{x}&3\\2\text{x}&5\end{vmatrix}$

Write the differential equation obtained emliminating the arbitrary constant $C$ in the equation $xy = C^2$.

Classify the following measures as scalar and vector:
45º