English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2580

Textbook Solutions20345

MCQ Online Mock Tests42

Important Solutions22654

Concept Notes & Videos608

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 (1+logx)/(x(2+logx)(3+logx))dx`

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 :

`∫_0^π(4x sin x)/(1+cos^2 x) dx`

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`

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

Evaluate of the following integral:

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

Evaluate of the following integral:

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

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:

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

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:

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

Evaluate the following integral:

\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]

Evaluate the following integral:

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

Evaluate the following integral:

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

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:

\[\int_{- a}^a \frac{1}{1 + a^x}dx\]`, a > 0`

Evaluate each of the following integral:

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

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

Evaluate the following integral:

\[\int_0^\pi x\sin x \cos^2 xdx\]

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:

\[\int_0^\pi \left( \frac{x}{1 + \sin^2 x} + \cos^7 x \right)dx\]

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

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

Evaluate: `int_ e^x ((2+sin2x))/cos^2 x dx`

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.

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

Evaluate the following:

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

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.

Notifications