हिंदी

Evaluate of the Following Integral: ∫ 3 2 Log 3 X D X - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate of the following integral:

\[\int 3^{2 \log_3} {}^x dx\]
योग

उत्तर

\[\int 3^{2 \log_{3^x}} dx\]
\[ = \int 3\log_3 x^2 dx\]
\[ = \int x^2 dx\]
\[ = \frac{x^3}{3} + C\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 19: Indefinite Integrals - Exercise 19.01 [पृष्ठ ४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Exercise 19.01 | Q 1.7 | पृष्ठ ४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate: `int1/(xlogxlog(logx))dx`


Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`


 

Evaluate `∫_0^(3/2)|x cosπx|dx`

 

 

find `∫_2^4 x/(x^2 + 1)dx`

 

Evaluate :

`int_e^(e^2) dx/(xlogx)`


Evaluate the integral by using substitution.

`int_0^1 sin^(-1) ((2x)/(1+ x^2)) dx`


Evaluate the integral by using substitution.

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


Evaluate the integral by using substitution.

`int_(-1)^1 dx/(x^2 + 2x  + 5)`


Evaluate the integral by using substitution.

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


Evaluate of the following integral: 

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

Evaluate of the following integral:

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

Evaluate: 

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

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

Evaluate the following integral:

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

Evaluate the following integral:

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

 


Evaluate the following integral:

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

Evaluate the following integral:

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

 


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:

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

Evaluate each of the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

\[\int_2^8 \frac{\sqrt{10 - x}}{\sqrt{x} + \sqrt{10 - x}}dx\]

Evaluate the following integral:

\[\int_{- \pi}^\pi \frac{2x\left( 1 + \sin x \right)}{1 + \cos^2 x}dx\]

Evaluate the following integral:

\[\int_{- 2}^2 \frac{3 x^3 + 2\left| x \right| + 1}{x^2 + \left| x \right| + 1}dx\]

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


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


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 ______.


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


`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.


`int_0^(pi4) sec^4x  "d"x` = ______.


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


Evaluate the following:

`int "dt"/sqrt(3"t" - 2"t"^2)`


Find: `int (dx)/sqrt(3 - 2x - x^2)`


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


Evaluate: `int x/(x^2 + 1)"d"x`


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×