मराठी

Evaluate: ∫ √ 1 + Cos 2 X 2 D X - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate: 

\[\int\sqrt{\frac{1 + \cos 2x}{2}}dx\]
बेरीज
Advertisements

उत्तर

\[\int\sqrt{\frac{1 + \cos 2x}{2}}dx\]
\[ \int\sqrt{\frac{\text{2 cos}^2 x}{2}}dx \left[ \therefore 1 + \cos2A = 2 \cos^2 A \right]\]
\[ = \int\ \text{cos  x dx}\]
\[ = \sin x + C\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 19: Indefinite Integrals - Exercise 19.01 [पृष्ठ ४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 19 Indefinite Integrals
Exercise 19.01 | Q 2.1 | पृष्ठ ४

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Evaluate :`int_0^(pi/2)1/(1+cosx)dx`

 


Evaluate: `int1/(xlogxlog(logx))dx`


Evaluate : `int1/(3+5cosx)dx`


Evaluate :

`∫_0^π(4x sin x)/(1+cos^2 x) dx`


Evaluate: `intsinsqrtx/sqrtxdx`

 


Evaluate the integral by using substitution.

`int_0^2 dx/(x + 4 - x^2)`


Evaluate the integral by using substitution.

`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`


Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`


Evaluate of the following integral: 

\[\int x^\frac{5}{4} dx\]

Evaluate: 

\[\int\frac{1}{a^x b^x}dx\]

Evaluate:

\[\int\frac{e\log \sqrt{x}}{x}dx\]

Evaluate the following definite integral:

\[\int_0^1 \frac{1}{\sqrt{\left( x - 1 \right)\left( 2 - x \right)}}dx\]

Evaluate the following integral:

\[\int\limits_1^2 \left| x - 3 \right| dx\]

Evaluate the following integral:

\[\int\limits_0^{\pi/2} \left| \cos 2x \right| dx\]

Evaluate the following integral:

\[\int\limits_2^8 \left| x - 5 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_{- \pi/2}^{\pi/2} \left\{ \sin \left| x \right| + \cos \left| x \right| \right\} dx\]

 


Evaluate the following integral:

\[\int\limits_1^4 \left\{ \left| x - 1 \right| + \left| x - 2 \right| + \left| x - 4 \right| \right\} dx\]

 


Evaluate each of the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{\sqrt{\tan x}}{\sqrt{\tan x} + \sqrt{\cot x}}dx\]

Evaluate each of the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}}dx\]

 


Evaluate each of the following integral:

\[\int_{- \frac{\pi}{4}}^\frac{\pi}{4} \frac{\tan^2 x}{1 + e^x}dx\]

 


Evaluate each of the following integral:

\[\int_{- \frac{\pi}{3}}^\frac{\pi}{3} \frac{1}{1 + e^\ tan\ x}dx\]

 


Evaluate each of the following integral:

\[\int_{- \frac{\pi}{4}}^\frac{\pi}{4} \frac{x^{11} - 3 x^9 + 5 x^7 - x^5 + 1}{\cos^2 x}dx\]

Evaluate the following integral:

\[\int_0^\frac{\pi}{2} \frac{\tan^7 x}{\tan^7 x + \cot^7 x}dx\]

Evaluate 

\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]


Evaluate the following integral:

\[\int_0^{2\pi} \sin^{100} x \cos^{101} xdx\]

 


Evaluate : 

\[\int\limits_0^{3/2} \left| x \sin \pi x \right|dx\]

Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .


Evaluate: `int_  e^x ((2+sin2x))/cos^2 x dx`


Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x"  d"x"`.


Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.


Find: `int_  (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.


If `I_n = int_0^(pi/4) tan^n theta  "d"theta " then " I_8 + I_6` equals ______.


Evaluate the following:

`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`


`int_0^1 x^2e^x dx` = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×