English

Evaluate of the Following Integral: (I) ∫ X 4 D X

Advertisements
Advertisements

Question

Evaluate of the following integral:

(i)  \[\int x^4 dx\]

 

Sum
Advertisements

Solution

\[\int x^4 dx\]
\[ = \frac{x^{4 + 1}}{4 + 1} + C\]
\[ = \frac{x^5}{5} + C\]

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 1.1 | Page 4

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate : `int1/(3+5cosx)dx`


 

find `∫_2^4 x/(x^2 + 1)dx`

 

Evaluate: `intsinsqrtx/sqrtxdx`

 


Evaluate the integral by using substitution.

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


If `f(x) = int_0^pi t sin  t  dt`, then f' (x) is ______.


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: 

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

Evaluate of the following integral: 

\[\int 3^x dx\]

Evaluate of the following integral:

\[\int \log_x \text{x  dx}\] 

Evaluate: 

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

Evaluate:

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

Evaluate: 

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

Evaluate:

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

Evaluate: 

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

Evaluate:

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

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

Evaluate the following integral:

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

Evaluate the following integral:

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

 


Evaluate the following integral:

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

 


Evaluate the following integral:

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

Evaluate the following integral:

\[\int\limits_1^4 \left\{ \left| x - 1 \right| + \left| x - 2 \right| + \left| x - 4 \right| \right\} dx\]

 


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:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{\sqrt{\tan x}}{\sqrt{\tan x} + \sqrt{\cot x}}dx\]

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 the following integral:

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

Evaluate the following integral:

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

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


`int_0^(pi4) sec^4x  "d"x` = ______.


Evaluate the following:

`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`


The value of `int_0^1 (x^4(1 - x)^4)/(1 + x^2) dx` is


Evaluate:

`int (1 + cosx)/(sin^2x)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×