Find the following integrals: ∫(2x2-3sinx+5x)dx - Mathematics

Question

Find the following integrals:

$\int (2 x^{2} - 3 \sin x + 5 \sqrt{x}) d x$

Sum

Solution

Let $I = \int (2 x^{2} - 3 \sin x + 5 \sqrt{5})$ dx

$I = 2 \int x^{2} d x - 3 \int \sin x d x + 5 \int x^{\frac{1}{2}}$ dx

$I = \frac{2}{3} x^{3} + 3 \cos x + \frac{10}{3} x^{\frac{3}{2}} + C$

shaalaa.com

Integration as an Inverse Process of Differentiation

Is there an error in this question or solution?

Q 17 Q 16 Q 18

Chapter 7: Integrals - Exercise 7.1 [Page 299]

APPEARS IN

NCERT Mathematics [English] Class 12

Chapter 7 Integrals
Exercise 7.1 | Q 17 | Page 299

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
Integration as an Inverse Process of Differentiation

video tutorial00:04:16

RELATED QUESTIONS

Write the antiderivative of $(3 \sqrt{x} + \frac{1}{\sqrt{x}}) .$

Find : $\int \frac{x^{2} + x + 1}{(x^{2} + 1) (x + 2)} d x$

Find an anti derivative (or integral) of the following function by the method of inspection.

Cos 3x

Find the following integrals:

$\int (4 e^{3 x} + 1)$

Find the following integrals:

$\int x^{2} (1 - \frac{1}{x^{2}}) d x$

Find the following integrals:

$\int (a x^{2} + b x + c) d x$

Find the following integrals:

$\int {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} d x$

Find the following integrals:

$\int (1 - x) \sqrt{x} d x$

Find the following integrals:

$\int \sqrt{x} (3 x^{2} + 2 x + 3) d x$

Find the following integrals:

$\int (2 x - 3 \cos x + e^{x}) d x$

Find the following integrals:

$\int \sec x (\sec x + \tan x) d x$

Find the following integrals:

$\int \frac{2 - 3 \sin x}{\cos^{2} x} d x .$

The anti derivative of $(\sqrt{x} + \frac{1}{\sqrt{x}})$ equals:

Integrate the function:

$\frac{1}{x - x^{3}}$

Integrate the function:

$\frac{1}{x^{2} {(x^{4} + 1)}^{\frac{3}{4}}}$

Integrate the function:

$\frac{\sin x}{\sin (x - a)}$

Integrate the function:

$\frac{1}{\cos (x + a) \cos (x + b)}$

Integrate the function:

$\frac{e^{x}}{(1 + e^{x}) (2 + e^{x})}$

Integrate the function:

$\cos^{3} x e^{\log \sin x}$

Integrate the function:

f' (ax + b) [f (ax + b)]ⁿ

Integrate the functions $\frac{\sin^{- 1} \sqrt{x} - \cos^{- 1} \sqrt{x}}{\sin^{- 1} \sqrt{x} + \cos^{- 1} \sqrt{x}}, x \in [0, 1]$

Integrate the function:

$\sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}}$

Integrate the function:

$\frac{2 + \sin 2 x}{1 + \cos 2 x} e^{x}$

Integrate the function:

$\frac{x^{2} + x + 1}{{(x + 1)}^{2} (x + 2)}$

Evaluate $\int \tan^{- 1} \sqrt{x} d x$

Find : $\int \frac{(x^{2} + 1) (x^{2} + 4)}{(x^{2} + 3) (x^{2} - 5)} d x$ .

The anti derivative of $(\sqrt{x} + \frac{1}{\sqrt{x}})$ is equals:

If $\frac{d}{d x} f (x) = 4 x^{3} - \frac{3}{x^{4}}$ , such that $f (2) = 0$ , then $f (x)$ is

$\int \frac{\sin^{2} x - \cos^{2} x}{\sin^{2} x \cos^{2} x} d x$ is equal to

$\int \frac{x d x}{(x - 1) (x - 2)}$ equals

$\int \sqrt{1 + x^{2}} d x$ is equal to

If the normal to the curve y(x) = $\int_{0}^{x} (2 t^{2} - 15 t + 10) d t$ at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.

$\frac{d}{d x} x^{\log x}$ = ______.

$\int \frac{d x}{\sqrt{5 x - 6 - x^{2}}}$ equals ______.

Anti-derivative of $\frac{\tan x - 1}{\tan x + 1}$ with respect to x is ______.

Find the following integrals: ∫(2x2-3sinx+5x)dx - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Find the following integrals: ∫(2x2-3sinx+5x)dx - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Solution