Advertisements
Advertisements
Question
` ∫ sin x \sqrt (1-cos 2x) dx `
Sum
Advertisements
Solution
` ∫ sin x . \sqrt (1-cos 2x) dx `
` ∫ sin x \sqrt (2 sin^2 x ) dx ` `[∴ 1 - cos 2A = 2 sin^2 A]`
` = \sqrt2 ∫ sin^2 x dx `
\[ = \sqrt{2}\int\left( \frac{1 - \cos 2x}{2} \right)dx\]
\[ = \frac{1}{\sqrt{2}}\int\left( 1 - \cos 2x \right)dx\]
\[ = \frac{1}{\sqrt{2}}\left[ x - \frac{\sin 2x}{2} \right] + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\frac{1}{\sqrt{x + 1} + \sqrt{x}} dx\]
\[\int\frac{1}{\sqrt{x + 3} - \sqrt{x + 2}} dx\]
`∫ cos ^4 2x dx `
\[\int\text{sin mx }\text{cos nx dx m }\neq n\]
\[\int\frac{1 - \sin 2x}{x + \cos^2 x} dx\]
\[\int 5^{x + \tan^{- 1} x} . \left( \frac{x^2 + 2}{x^2 + 1} \right) dx\]
\[\int\frac{x^2}{\sqrt{1 - x}} dx\]
\[\int {cosec}^4 \text{ 3x } \text{ dx } \]
\[\int \cot^5 x \text{ dx }\]
\[\int \sin^7 x \text{ dx }\]
\[\int\frac{e^x}{1 + e^{2x}} dx\]
\[\int\frac{1}{x \left( x^6 + 1 \right)} dx\]
\[\int\frac{\left( 3 \sin x - 2 \right) \cos x}{5 - \cos^2 x - 4 \sin x} dx\]
\[\int\frac{x^2 + 1}{x^2 - 5x + 6} dx\]
\[\int\frac{5 \cos x + 6}{2 \cos x + \sin x + 3} \text{ dx }\]
\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]
\[\int x^3 \text{ log x dx }\]
\[\int x e^x \text{ dx }\]
\[\int \log_{10} x\ dx\]
\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx }\]
\[\int \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}} dx\]
\[\int e^x \left( \cos x - \sin x \right) dx\]
\[\int e^x \left( \frac{x - 1}{2 x^2} \right) dx\]
\[\int x\sqrt{x^4 + 1} \text{ dx}\]
\[\int\sqrt{x^2 - 2x} \text{ dx}\]
\[\int\left( 4x + 1 \right) \sqrt{x^2 - x - 2} \text{ dx }\]
\[\int\frac{5 x^2 - 1}{x \left( x - 1 \right) \left( x + 1 \right)} dx\]
\[\int\frac{x}{\left( x^2 - a^2 \right) \left( x^2 - b^2 \right)} dx\]
If \[\int\frac{1}{5 + 4 \sin x} dx = A \tan^{- 1} \left( B \tan\frac{x}{2} + \frac{4}{3} \right) + C,\] then
\[\int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\} dx =\]
\[\int\frac{1}{e^x + 1} \text{ dx }\]
\[\int \sin^5 x\ dx\]
\[\int\frac{1}{4 x^2 + 4x + 5} dx\]
\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]
\[\int\frac{\cos x}{\frac{1}{4} - \cos^2 x} \text{ dx }\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int\frac{1}{2 + \cos x} \text{ dx }\]
\[\int\sqrt{3 x^2 + 4x + 1}\text{ dx }\]
\[\int \sin^3 \left( 2x + 1 \right) \text{dx}\]
\[\int\frac{3x + 1}{\sqrt{5 - 2x - x^2}} \text{ dx }\]
