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

प्रश्न

Evaluate of the following integral:

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

योग

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

Evaluation of Definite Integrals by Substitution

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 1.6 Q 1.5 Q 1.7

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]

view
वीडियो ट्यूटोरियल For All Subjects
Evaluation of Definite Integrals by Substitution

video tutorial00:18:12

संबंधित प्रश्न

Evaluate: `int1/(xlogxlog(logx))dx`

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

Evaluate `int_(-1)^2|x^3-x|dx`

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 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^(pi/2) (sin x)/(1+ cos^2 x) dx`

`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:

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

Evaluate of the following integral:

\[\int \log_x \text{x dx}\]

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:

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

Evaluate:

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

Evaluate the following definite integral:

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