English
CBSECommerce (English Medium) Class 12
Question Papers3000
Textbook Solutions36125
MCQ Online Mock Tests42
Important Solutions23873
Concept Notes & Videos697
Time Tables25
Syllabus

Evaluate of the Following Integral: ∫ 3 X D X

Advertisements
Advertisements

Question

Evaluate of the following integral: 

\[\int 3^x dx\]
Sum
Advertisements

Solution

\[\int 3^x dx\]
\[ = \frac{3^x}{\ln 3} + C\]

shaalaa.com
Evaluation of Definite Integrals
  Is there an error in this question or solution?
Q 1.5
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 1.5 | Page 4

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate: `int1/(xlogxlog(logx))dx`


Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 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 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_0^2 dx/(x + 4 - x^2)`


Evaluate of the following integral:

(i)  \[\int x^4 dx\]

 


Evaluate of the following integral: 

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

Evaluate of the following integral: 

\[\int\frac{1}{x^5}dx\]

Evaluate of the following integral:

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

Evaluate of the following integral:

\[\int \log_x \text{x  dx}\] 

Evaluate: 

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

Evaluate: 

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

Evaluate:

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

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:

\[\int\limits_{- \pi/4}^{\pi/4} \left| \sin x \right| dx\]

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:

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

Evaluate each of the following integral:

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

 


Evaluate each of the following integral:

\[\int_{- a}^a \frac{1}{1 + a^x}dx\]`, a > 0`

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 the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{1}{1 + \cot^\frac{3}{2} x}dx\]

 


Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate : 

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

`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?


`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` = ______.


`int_0^1 x^2e^x dx` = ______.


In Method: Resubstitution, what should be done first?


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


What is the value of \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\]?


Share
Notifications

Englishहिंदीमराठी
Login
Create free account


      Forgot password?
Course
Use app×