मराठी

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

Advertisements
Advertisements

प्रश्न

Evaluate of the following integral:

\[\int 3^{2 \log_3} {}^x dx\]
बेरीज

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
  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 1.7 | पृष्ठ ४

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

 

Evaluate `int_(-1)^2|x^3-x|dx`

 

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`


 

find `∫_2^4 x/(x^2 + 1)dx`

 

Evaluate :

`∫_0^π(4x sin x)/(1+cos^2 x) dx`


Evaluate :

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


Evaluate: `intsinsqrtx/sqrtxdx`

 


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 xsqrt(x+2)`  (Put x + 2 = `t^2`)


Evaluate the integral by using substitution.

`int_(-1)^1 dx/(x^2 + 2x  + 5)`


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


Evaluate: 

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

Evaluate : 

\[\int\frac{e^{6 \log_e x} - e^{5 \log_e x}}{e^{4 \log_e x} - e^{3 \log_e x}}dx\]

Evaluate: 

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

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

Evaluate the following definite integral:

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

Evaluate the following integral:

\[\int\limits_0^3 \left| 3x - 1 \right| dx\]

 


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:

\[\int\limits_0^4 \left| x - 1 \right| dx\]

Evaluate the following integral:

\[\int\limits_0^4 \left( \left| x \right| + \left| x - 2 \right| + \left| x - 4 \right| \right) dx\]

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:

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

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

Evaluate the following integral:

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

Evaluate the following integral:

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

 


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


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


Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .


Evaluate:  `int_-1^2 (|"x"|)/"x"d"x"`.


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


Evaluate:

`int (1 + cosx)/(sin^2x)dx`


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×