English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2593

Textbook Solutions20345

MCQ Online Mock Tests42

Important Solutions23141

Concept Notes & Videos614

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

Advertisements

Advertisements

Question

Evaluate of the following integral:

\[\int 3^x dx\]

Sum

Advertisements

Solution

\[\int 3^x dx\]
\[ = \frac{3^x}{\ln 3} + C\]

shaalaa.com

Evaluation of Definite Integrals by Substitution

Is there an error in this question or solution?

Q 1.5 Q 1.4 Q 1.6

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

Evaluate : `int1/(3+5cosx)dx`

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

Evaluate :

`∫_0^π(4x sin x)/(1+cos^2 x) 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 ______.

Evaluate of the following integral:

(i) \[\int x^4 dx\]

Evaluate of the following integral:

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

Evaluate of the following integral:

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

Evaluate of the following integral:

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

Evaluate:

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

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:

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

Evaluate:

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

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

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

\[\int\limits_2^8 \left| x - 5 \right| dx\]

Evaluate the following integral:

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

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:

\[\int_{- \frac{\pi}{3}}^\frac{\pi}{3} \frac{1}{1 + e^\ tan\ x}dx\]

Evaluate the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{1}{1 + \cot^\frac{3}{2} x}dx\]

Evaluate the following integral:

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

Evaluate the following integral:

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

Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .

Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x" d"x"`.

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

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

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

Evaluate the following:

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

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`.

Evaluate:

`int (1 + cosx)/(sin^2x)dx`

If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.

Notifications