English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2593

Textbook Solutions20345

MCQ Online Mock Tests42

Important Solutions23141

Concept Notes & Videos614

Evaluate of the Following Integral: ∫ 1 X 5 D X - Mathematics

Advertisements

Advertisements

Question

Evaluate of the following integral:

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

Sum

Advertisements

Solution

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

shaalaa.com

Evaluation of Definite Integrals by Substitution

Is there an error in this question or solution?

Q 1.3 Q 1.2 Q 1.4

Chapter 19: Indefinite Integrals - Exercise 19.01 [Page 4]

APPEARS IN

RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.01 | Q 1.3 | Page 4

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
Evaluation of Definite Integrals by Substitution

video tutorial00:18:12

RELATED QUESTIONS

Evaluate :`int_0^(pi/2)1/(1+cosx)dx`

Evaluate: `int1/(xlogxlog(logx))dx`

Evaluate : `int1/(3+5cosx)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^(pi/2) sqrt(sin phi) cos^5 phidphi`

Evaluate the integral by using substitution.

`int_0^2 xsqrt(x+2)` (Put x + 2 = `t^2`)

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:

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

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:

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

Evaluate the following integral:

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

Evaluate the following integral:

\[\int\limits_2^8 \left| x - 5 \right| dx\]

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:

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

Evaluate each of the following integral:

\[\int_{- \frac{\pi}{3}}^\frac{\pi}{3} \frac{1}{1 + e^\ tan\ x}dx\]

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

\[\int_0^{2\pi} \sin^{100} x \cos^{101} xdx\]

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

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

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}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_0^1 sin^-1 ((2x)/(1 + x^2))"d"x` = ______.

Notifications