मराठी

Evaluate: dx∫cos−1⁡(sin⁡x)dx - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate:

\[\int \cos^{-1} \left(\sin x \right) \text{dx}\]

बेरीज
Advertisements

उत्तर

\[\int \cos^{-1} \left(\sin x \right)\text{ dx }\]

\[= \int \cos^{-1} \left( \cos\left( \frac{\pi}{2} - x \right) \right) \text{ dx }\]

\[ = \int \left(\frac{\pi}{2} - x \right) dx\]

\[ = \frac{\pi}{2}x - \frac{1}{2} x^2 + c\]

\[\text{Hence,}\int \cos^{-1} \left(\sin x \right)\text{ dx } = \frac{\pi}{2}x - \frac{1}{2} x^2 + c\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 19: Indefinite Integrals - Very Short Answers [पृष्ठ १९८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 19 Indefinite Integrals
Very Short Answers | Q 60 | पृष्ठ १९८

संबंधित प्रश्‍न

\[\int\frac{x}{\sqrt{x + 4}} dx\]

\[\int\frac{\cos 2x}{\left( \cos x + \sin x \right)^2} dx\]

\[\int\frac{1 + \tan x}{1 - \tan x} dx\]

\[\int\frac{1}{x \log x} dx\]

\[\int\frac{1}{e^x + 1} dx\]

\[\int\frac{\cos 2x + x + 1}{x^2 + \sin 2x + 2x} dx\]

\[\int\frac{1}{\cos\left( x + a \right) \cos\left( x + b \right)}dx\]

` ∫  {1+tan}/{ x + log  sec  x   dx} `

\[\int\frac{e^x}{\left( 1 + e^x \right)^2} dx\]

\[\int\frac{x^3}{\left( x^2 + 1 \right)^3} dx\]

Evaluate the following integrals:

\[\int\frac{\sqrt{1 + x^2}}{x^4}dx\]

Evaluate the following integrals:

\[\int\frac{1}{\left( x^2 + 2x + 10 \right)^2}dx\]

 


\[\int\frac{x^3 - 3x}{x^4 + 2 x^2 - 4}dx\]

Evaluate the following integrals:

\[\int\frac{\log x}{\left( x + 1 \right)^2}dx\]

 


Evaluate the following integrals:

\[\int\left( x + 3 \right)\sqrt{3 - 4x - x^2} \text{  dx }\]

\[\int(3x + 1) \sqrt{4 - 3x - 2 x^2} \text{  dx }\]

Evaluate the following integral:

\[\int\frac{x^2}{\left( x^2 + 4 \right)\left( x^2 + 9 \right)}dx\]

Evaluate the following integral:

\[\int\frac{x^3 + x + 1}{x^2 - 1}dx\]

Evaluate the following integral:

\[\int\frac{1}{x\left( x^3 + 8 \right)}dx\]

 


Evaluate the following integral:

\[\int\frac{2 x^2 + 1}{x^2 \left( x^2 + 4 \right)}dx\]

Evaluate the following integrals:

\[\int\frac{x^2}{(x - 1) ( x^2 + 1)}dx\]

Evaluate the following integral:

\[\int\frac{x^2}{x^4 + x^2 - 2}dx\]

\[\int\frac{x^2 + 1}{x^4 - x^2 + 1} \text{ dx }\]

Evaluate:\[\int\frac{x^2}{1 + x^3} \text{ dx }\] .


Evaluate:\[\int \sec^2 \left( 7 - 4x \right) \text{ dx }\]


Evaluate:\[\int\frac{e\tan^{- 1} x}{1 + x^2} \text{ dx }\]


Evaluate: \[\int\frac{1}{\sqrt{1 - x^2}} \text{ dx }\]


Evaluate: \[\int\frac{x + \cos6x}{3 x^2 + \sin6x}\text{ dx }\]


Evaluate:

`∫ (1)/(sin^2 x cos^2 x) dx`


Evaluate : \[\int\frac{1}{x(1 + \log x)} \text{ dx}\]


Evaluate: `int_  (x + sin x)/(1 + cos x )  dx`


Evaluate the following:

`int ("d"x)/sqrt(16 - 9x^2)`


Evaluate the following:

`int sqrt(5 - 2x + x^2) "d"x`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×