English

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

Advertisements
Advertisements

Question

Evaluate of the following integral:

\[\int 3^{2 \log_3} {}^x dx\]
Sum
Advertisements

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 18: Indefinite Integrals - Exercise 19.01 [Page 4]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 18 Indefinite Integrals
Exercise 19.01 | Q 1.7 | Page 4

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate: `int1/(xlogxlog(logx))dx`


 

Evaluate `∫_0^(3/2)|x cosπx|dx`

 

 

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`


If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.


Evaluate :

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


Evaluate the integral by using substitution.

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


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_0^(pi/2) (sin x)/(1+ cos^2 x) 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 of the following integral: 

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

Evaluate of the following integral: 

\[\int 3^x dx\]

Evaluate of the following integral:

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

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:

\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]

 


Evaluate the following integral:

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

 


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:

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

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

Evaluate the following integral:

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

Evaluate 

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


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


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


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


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


Evaluate the following:

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


Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is


Under Method: Changing the Limits, what does the lower limit \[a\] become?


After using \[t=\tan^{-1}x\] in \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\], which integral results?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×