Evaluate the following integrals: ^ -1 ( )dx - Vidyadip

Question

Evaluate the following integrals:
$\int\cos^{-1}(\sin\text{x})\text{dx}$

✓

Answer

$\int\cos^{-1}(\sin\text{x})\text{dx}$
$=\int\cos^{-1}\Big(\cos\Big(\frac{\pi}{2}-\text{x}\Big)\Big)\text{dx}$ $\Big[\therefore\ \sin\text{x}=\cos\Big(\frac{\pi}{2}-\text{x}\Big)\Big]$
$=\int\Big(\frac{\pi}{2}-\text{x}\Big)\text{dx}$
$=\frac{\pi\text{x}}{2}-\frac{\text{x}^2}{2}+\text{C}$

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 "2 Marks Questions" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{y}=\text{x}+\text{e}^\text{x},$ find $\frac{\text{d}^2\text{x}}{\text{dy}^2}.$

Evaluate the definite integral in Exercise:
$\int\limits_{2}^{3}\frac{\text{x}\ \text{dx}}{\text{x}^{2}+1}$

Write the value of $\big[\hat{\text{i}}-\hat{\text{j }}\hat{\text{j}}-\hat{\text{k }}\hat{\text{k}}-\hat{\text{i}}\big].$

Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=4$

If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2=144$ and $|\vec{\text{a}}|=4,$ find $\big|\vec{\text{b}}\big|.$

Evaluate the definite integral $\int_0^{\frac{\pi}{4}} \tan x d x$.

Evaluate:
$\int\frac{\text{e}^{6\log_\text{e}\text{x}}-\text{e}^{5\log_\text{e}\text{x}}}{\text{e}^{4\log_\text{e}\text{x}}-\text{e}^{3\log_\text{e}\text{x}}}\text{dx}$

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

$\text{y}=\text{a e}^{\text{x}}+\text{b e}^{-\text{x}}+\text{x}^2$

$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\frac{\text{dy}}{\text{dx}}-\text{xy}+\text{x}^2-2=0$

Consider the following information regarding the number of men and women workers in three factories I, II and III

	Men workers	Women workers
I	30	25
II	25	31
III	27	26

Represent the above information in the form of a 3 $\times$ 2 matrix. What does the entry in the third row and second column represent?

If x and y are connected parametrically by the equation $x = \cos \theta - \cos 2\theta ,y = \sin \theta - \sin 2\theta $, without eliminating the parameter, find $\frac{{dy}}{{dx}}.$