English

Evaluate: ∫ 2 1 − Cos 2 X D X - Mathematics

Advertisements
Advertisements

Question

Evaluate:  \[\int\frac{2}{1 - \cos2x}\text{ dx }\]

Sum
Advertisements

Solution

\[\int\frac{2}{1 - \cos2x}dx = \int\frac{2}{2 \sin^2 x}dx\]
\[ = \int {cosec}^2 \text{ x dx }\]
\[ = - \cot x + c\]
\[\text{ Hence, } \int\frac{2}{1 - \cos2x}dx = - \cot x + c .\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 19: Indefinite Integrals - Very Short Answers [Page 198]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 19 Indefinite Integrals
Very Short Answers | Q 58 | Page 198

RELATED QUESTIONS

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

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

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

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

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

\[\int\frac{sec x}{\log \left( \text{sec x }+ \text{tan x} \right)} dx\]

\[\int\frac{{cosec}^2 x}{1 + \cot x} dx\]

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

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

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

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

\[\int\frac{1 + \sin x}{\sqrt{x - \cos x}} dx\]

\[\int\frac{1}{\sqrt{1 - x^2} \left( \sin^{- 1} x \right)^2} dx\]


\[\int\frac{\cot x}{\sqrt{\sin x}} dx\]


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

Evaluate the following integrals:

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

Evaluate the following integrals:

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

 


Evaluate the following integrals:

\[\int\frac{5x - 2}{1 + 2x + 3 x^2} \text{ dx }\]

\[\int\frac{1}{5 - 4 \cos x} \text{ dx }\]

Evaluate the following integrals:

\[\int e^{2x} \left( \frac{1 - \sin2x}{1 - \cos2x} \right)dx\]

Evaluate the following integral :-

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

Evaluate the following integral:

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

\[\int\frac{\cos x}{\left( 1 - \sin x \right) \left( 2 - \sin x \right)} dx\]

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

Write a value of

\[\int\frac{\left( \log x \right)^n}{x} \text{ dx }\]

Evaluate:

\[\int\frac{x^2 + 4x}{x^3 + 6 x^2 + 5} \text{ dx }\]

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

 


Evaluate:\[\int\frac{\sin \sqrt{x}}{\sqrt{x}} \text{ dx }\]


Evaluate:\[\int\frac{\cos \sqrt{x}}{\sqrt{x}} \text{ dx }\]


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


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


Evaluate:

`∫ (1)/(sin^2 x cos^2 x) dx`


Evaluate the following:

`int (3x - 1)/sqrt(x^2 + 9) "d"x`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×