हिंदी

Evaluate of the Following Integral: ∫ 1 3 √ X 2 D X

Advertisements
Advertisements

प्रश्न

Evaluate of the following integral:

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

उत्तर

\[\int\frac{dx}{\sqrt[3]{x^2}}\]
\[ = \int\frac{dx}{x^{2/3}}\]
\[ = \int x^{- 2/3} dx\]
\[ = \frac{x^{- \frac{2}{3} + 1}}{- \frac{2}{3} + 1} + C\]
\[ = 3 x^\frac{1}{3} + C\]
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 18: Indefinite Integrals - Exercise 19.01 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 18 Indefinite Integrals
Exercise 19.01 | Q 1.6 | पृष्ठ ४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate : `int1/(3+5cosx)dx`


 

Evaluate `∫_0^(3/2)|x cosπx|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 sin^(-1) ((2x)/(1+ x^2)) dx`


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)`


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: 

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

Evaluate: 

\[\int\sqrt{\frac{1 + \cos 2x}{2}}dx\]

Evaluate:

\[\int\sqrt{\frac{1 - \cos 2x}{2}}dx\]

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:

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

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:

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

 


Evaluate the following integral:

\[\int\limits_0^4 \left( \left| x \right| + \left| x - 2 \right| + \left| x - 4 \right| \right) dx\]

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:

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

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 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:

\[\int_{- \frac{\pi}{4}}^\frac{\pi}{4} \frac{x^{11} - 3 x^9 + 5 x^7 - x^5 + 1}{\cos^2 x}dx\]

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

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:

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

Evaluate the following integral:

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

 


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


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


`int_0^1 x(1 - x)^5 "dx" =` ______.


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


Evaluate the following:

`int "dt"/sqrt(3"t" - 2"t"^2)`


`int_0^1 x^2e^x dx` = ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×