English

Evaluate of the Following Integral: ∫ 1 X 3 / 2 D X - Mathematics

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
  Is there an error in this question or solution?
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 1.4 | Page 4

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate:  `int (1+logx)/(x(2+logx)(3+logx))dx`


Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`


Evaluate : `int1/(3+5cosx)dx`


 

Evaluate `∫_0^(3/2)|x cosπx|dx`

 

 

find `∫_2^4 x/(x^2 + 1)dx`

 

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`)


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


Evaluate of the following integral:

(i)  \[\int x^4 dx\]

 


Evaluate of the following integral: 

\[\int x^\frac{5}{4} dx\]

Evaluate of the following integral: 

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

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:

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

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

Evaluate the following definite integral:

\[\int_0^1 \frac{1}{\sqrt{\left( x - 1 \right)\left( 2 - x \right)}}dx\]

Evaluate the following integral:

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

Evaluate the following integral:

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

 


Evaluate the following integral:

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

Evaluate each of the following integral:

\[\int_0^{2\pi} \frac{e^\ sin x}{e^\ sin x + e^{- \ sin x}}dx\]

 


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 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:

\[\int_{- \frac{3\pi}{2}}^{- \frac{\pi}{2}} \left\{ \sin^2 \left( 3\pi + x \right) + \left( \pi + x \right)^3 \right\}dx\]

Evaluate the following integral:

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

 


Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .


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


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


`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.


`int_0^1 sin^-1 ((2x)/(1 + x^2))"d"x` = ______.


Find: `int (dx)/sqrt(3 - 2x - x^2)`


`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`


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×