Find the following integrals: ∫(ax2+bx+c)dx - Mathematics

Question

Find the following integrals:

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

Sum

Solution

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

$= a \int x^{2} a x + b \int x d x + c \int 1 d x$

$= \frac{a x^{3}}{3} + \frac{b x^{2}}{2} + c x + C$

shaalaa.com

Integration as an Inverse Process of Differentiation

Is there an error in this question or solution?

Q 8 Q 7 Q 9

Chapter 7: Integrals - Exercise 7.1 [Page 299]

APPEARS IN

NCERT Mathematics [English] Class 12

Chapter 7 Integrals
Exercise 7.1 | Q 8 | 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

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

If $f (x) = \int_{0}^{x} t \sin t d t$ , then write the value of f ' (x).

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

sin 2x

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

Cos 3x

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

e^2x

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

sin 2x – 4 e^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:

$\int \frac{x^{3} + 5 x^{2} - 4}{x^{2}} d x$

Find the following integrals:

$\int \frac{x^{3} - x^{2} + x - 1}{x - 1} d x$

Find the following integrals:

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

Integrate the function:

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

Integrate the function:

$\frac{1}{\sqrt{x + a} + \sqrt{x + b}}$

Integrate the function:

$\frac{1}{x^{\frac{1}{2}} + x^{\frac{1}{3}}} [Hint: \frac{1}{x^{\frac{1}{2}} + x^{\frac{1}{3}}} = \frac{1}{x^{\frac{1}{3}} (1 + x^{\frac{1}{6}})}, put x = t^{6}]$

Integrate the function:

$\frac{5 x}{(x + 1) (x^{2} + 9)}$

Integrate the function:

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

Integrate the function:

$\frac{e^{5 \log x} - e^{4 \log x}}{e^{3 \log x} - e^{2 \log x}}$

Integrate the function:

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

Integrate the function:

$\frac{x^{3}}{\sqrt{1 - x^{8}}}$

Integrate the function:

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

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:

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

Integrate the function:

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

Integrate the function:

$\frac{\sqrt{x^{2} + 1} [\log (x^{2} + 1) - 2 \log x]}{x^{4}}$

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

Evaluate: $\int \frac{1 - \cos x}{\cos x (1 + \cos x)} d x$

$\int \frac{d x}{\sin^{2} x \cos^{2} x} d x$ equals

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

$f x^{2} e^{x^{3}} d x$ equals

$\int \sqrt{x^{2} - 8 x + 7} d x$ is equal to:-

If y = $x^{{(\sin x)}^{x^{{(\sin x)}^{x^{... \infty}}}}}$ , then $\frac{d y}{d x}$ at x = $\frac{π}{2}$ is equal to ______.

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

Find the following integrals: ∫(ax2+bx+c)dx - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Find the following integrals: ∫(ax2+bx+c)dx - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Solution