∫ 1 √ a 2 − B 2 X 2 D X - Mathematics

Question

\int \frac{1}{\sqrt{a^{2} - b^{2} x^{2}}} d x

Sum

Solution

$\int \frac{d x}{\sqrt{a^{2} - b^{2} x^{2}}}$
$= \int \frac{d x}{\sqrt{b^{2} (\frac{a^{2}}{b^{2}} - x^{2})}}$
$= \frac{1}{b} \int \frac{d x}{\sqrt{{(\frac{a}{b})}^{2} - x^{2}}}$
$= \frac{1}{b} \sin^{- 1} (\frac{x b}{a}) + C$

shaalaa.com

Indefinite Integral Problems

Is there an error in this question or solution?

Q 7 Q 6 Q 8

Chapter 19: Indefinite Integrals - Exercise 19.14 [Page 83]

APPEARS IN

RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.14 | Q 7 | Page 83

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
Indefinite Integral Problems

video tutorial00:39:37

RELATED QUESTIONS

\int \frac{\sin^{2} x}{1 + \cos x} dx

\int \frac{\cos^{2} x - \sin^{2} x}{\sqrt{1} + \cos 4 x} d x

\int \frac{1}{1 + \cos 2 x} d x

\int \sin x \sqrt{1 + \cos 2 x} d x

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

\int \frac{2 x + 1}{\sqrt{3 x + 2}} d x

\int \frac{sin (x - α)}{sin (x + α)} d x

$\int \frac{\sin 2 x}{a \cos^{2} x + b \sin^{2} x}$ dx

\int \frac{1 - \sin 2 x}{x + \cos^{2} x} d x

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

$\int \frac{e^{m \sin^{- 1} x}}{\sqrt{1 - x^{2}}}$ dx

\int \frac{e^{2 x}}{1 + e^{x}} d x

\int \sqrt{e^{x} - 1} dx

$\int \tan^{5} x d x$

\int \frac{1}{\sqrt{8 + 3 x - x^{2}}} d x

\int \frac{x}{\sqrt{x^{4} + a^{4}}} d x

\int \frac{\sin 2 x}{\sqrt{\cos^{4} x - \sin^{2} x + 2}} d x

\int log (x + 1) dx

\int x e^{x} dx

\int \sin x \log (cos x ) d x

\int \frac{x + \sin x}{1 + \cos x} dx

\int \cos^{3} \sqrt{x} d x

\int e^{x} (\cos x - \sin x) d x

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

\int \frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x / 2} dx

\int e^{x} \cdot \frac{\sqrt{1 - x^{2}} \sin^{- 1} x + 1}{\sqrt{1 - x^{2}}} dx

∴

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

\int \frac{x + 1}{x (1 + x e^{x})} d x

\int \frac{1}{x^{4} + 3 x^{2} + 1} dx

\int \frac{x^{2}}{(x - 1) \sqrt{x + 2}} dx

\int \frac{x}{(x - 3) \sqrt{x + 1}} d x

\int \frac{1}{\cos x + \sqrt{3} \sin x} dx

is equal to

\int e^{x} (1 - \cot x + \cot^{2} x) d x =

\int e^{x} {f (x) + f^{'} (x)} d x =

The value of $\int \frac{\sin x + \cos x}{\sqrt{1 - \sin 2 x}} d x$ is equal to

\int {cosec}^{2} x {cos}^{2} 2x  dx

\int \frac{\sin^{5} x}{\cos^{4} x} dx

$\int (1 + x^{2}) \cos 2 x d x$

\int \frac{\log (\log x)}{x} dx

∫ 1 √ a 2 − B 2 X 2 D X - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

∫ 1 √ a 2 − B 2 X 2 D X - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Solution