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 3 / 2 D X

Advertisements

Advertisements

Question

Evaluate of the following integral:

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

Sum

Advertisements

Solution

\[\int\frac{dx}{x^{3/2}}\]
\[ = \int x^{- 3/2} dx\]
\[ = \left[ \frac{x^{- \frac{3}{2} + 1}}{\frac{- 3}{2} + 1} \right] + C\]
\[ = \left[ \frac{x^{- \frac{1}{2}}}{- \frac{1}{2}} \right] + C\]
\[ = - \frac{2}{\sqrt{x}} + C\]

shaalaa.com

Evaluation of Definite Integrals by Substitution

Is there an error in this question or solution?

Q 1.4 Q 1.3 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 1.4 | 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 `∫_0^(3/2)|x cosπx|dx`

find `∫_2^4 x/(x^2 + 1)dx`

If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.

Evaluate the integral by using substitution.

`int_0^1 x/(x^2 +1)`dx

Evaluate the integral by using substitution.

`int_(-1)^1 dx/(x^2 + 2x + 5)`

`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:

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

Evaluate of the following integral:

\[\int 3^x dx\]

Evaluate of the following integral:

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

Evaluate of the following integral:

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

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:

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

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

Evaluate the following integral:

\[\int\limits_0^3 \left| 3x - 1 \right| dx\]

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

\[\int\limits_0^4 \left| x - 1 \right| dx\]

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:

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

\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]

Evaluate the following integral:

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

Evaluate the following integral:

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

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 the following integral:

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

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"`.

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 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

`int_0^1 x^2e^x dx` = ______.

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

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

Notifications