English

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
  Is there an error in this question or solution?
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]

RELATED QUESTIONS

Evaluate: `int1/(xlogxlog(logx))dx`


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


Evaluate: `intsinsqrtx/sqrtxdx`

 


Evaluate the integral by using substitution.

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


Evaluate the integral by using substitution.

`int_0^2 xsqrt(x+2)`  (Put x + 2 = `t^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 `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) 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:

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

Evaluate the following integral:

\[\int\limits_{- 6}^6 \left| x + 2 \right| dx\]

 


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:

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

Evaluate the following integral:

\[\int\limits_1^4 \left\{ \left| x - 1 \right| + \left| x - 2 \right| + \left| x - 4 \right| \right\} dx\]

 


Evaluate 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:

\[\int_{- \frac{\pi}{4}}^\frac{\pi}{4} \frac{\tan^2 x}{1 + e^x}dx\]

 


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 each of the following integral:

\[\int_{- \frac{\pi}{2}}^\frac{\pi}{2} \frac{\cos^2 x}{1 + e^x}dx\]

Evaluate the following integral:

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

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:

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

Evaluate 

\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]


Evaluate the following integral:

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

 


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


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


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


`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?


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


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


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


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×