English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2580

Textbook Solutions20345

MCQ Online Mock Tests42

Important Solutions22654

Concept Notes & Videos608

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: `int1/(xlogxlog(logx))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`

Evaluate: `intsinsqrtx/sqrtxdx`

Evaluate the integral by using substitution.

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

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

Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`

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 :

\[\int\frac{e^{6 \log_e x} - e^{5 \log_e x}}{e^{4 \log_e x} - e^{3 \log_e x}}dx\]

Evaluate:

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

Evaluate the following integral:

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

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:

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

Evaluate the following integral:

\[\int\limits_{- 5}^0 f\left( x \right) dx, where\ f\left( x \right) = \left| x \right| + \left| x + 2 \right| + \left| x + 5 \right|\]

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

\[\int_0^\pi \left( \frac{x}{1 + \sin^2 x} + \cos^7 x \right)dx\]

Evaluate the following integral:

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

Evaluate the following integral:

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

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

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

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.

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

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

Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.

Evaluate: `int x/(x^2 + 1)"d"x`

Notifications