English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers3000

Textbook Solutions35049

MCQ Online Mock Tests42

Important Solutions23871

Concept Notes & Videos707

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

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 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 1.3 | 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 (1+logx)/(x(2+logx)(3+logx))dx`

Evaluate `∫_0^(3/2)|x cosπx|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^(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 the integral by using substitution.

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

The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.

`int 1/(1 + cos x)` dx = _____

A) `tan(x/2) + c`

B) `2 tan (x/2) + c`

C) -`cot (x/2) + c`

D) -2 `cot (x/2)` + c

Evaluate of the following integral:

(i) \[\int x^4 dx\]

Evaluate of the following integral:

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

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 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:

\[\int\limits_1^2 \left| x - 3 \right| dx\]

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 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:

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

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

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

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

Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .

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

Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x" d"x"`.

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

Evaluate the following:

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

Notifications