हिंदी

Evaluate: ∫ √ 1 + Cos 2 X 2 D X

Advertisements
Advertisements

प्रश्न

Evaluate: 

\[\int\sqrt{\frac{1 + \cos 2x}{2}}dx\]
योग
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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 18: Indefinite Integrals - Exercise 19.01 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 18 Indefinite Integrals
Exercise 19.01 | Q 2.1 | पृष्ठ ४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`


Evaluate: `intsinsqrtx/sqrtxdx`

 


Evaluate the integral by using substitution.

`int_0^2 xsqrt(x+2)`  (Put x + 2 = `t^2`)


Evaluate the integral by using substitution.

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


The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.


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


Evaluate: 

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

Evaluate:

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

Evaluate:

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

Evaluate the following integral:

\[\int\limits_{- 6}^6 \left| x + 2 \right| dx\]

 


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:

\[\int\limits_{- 5}^0 f\left( x \right) dx, where\ f\left( x \right) = \left| x \right| + \left| x + 2 \right| + \left| x + 5 \right|\]

 


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:

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

\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]

Evaluate the following integral:

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

Evaluate the following integral:

\[\int_0^\pi x\sin x \cos^2 xdx\]

Evaluate the following integral:

\[\int_{- \frac{3\pi}{2}}^{- \frac{\pi}{2}} \left\{ \sin^2 \left( 3\pi + x \right) + \left( \pi + x \right)^3 \right\}dx\]

Evaluate the following integral:

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

 


Evaluate the following integral:

\[\int_0^\frac{\pi}{2} \frac{a\sin x + b\sin x}{\sin x + \cos x}dx\]

 


Evaluate : 

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

Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .


Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .


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


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


`int_0^1 x(1 - x)^5 "dx" =` ______.


`int_0^(pi4) sec^4x  "d"x` = ______.


`int_0^1 sin^-1 ((2x)/(1 + x^2))"d"x` = ______.


Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.


If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×