Advertisements
Advertisements
प्रश्न
` ∫ sin x \sqrt (1-cos 2x) dx `
योग
Advertisements
उत्तर
` ∫ 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
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\frac{5 \cos^3 x + 6 \sin^3 x}{2 \sin^2 x \cos^2 x} dx\]
\[\int\frac{x^2 + 5x + 2}{x + 2} dx\]
\[\int\frac{\cos x}{\cos \left( x - a \right)} dx\]
\[\int\sqrt{\frac{1 - \sin 2x}{1 + \sin 2x}} dx\]
\[\int\frac{- \sin x + 2 \cos x}{2 \sin x + \cos x} dx\]
` = ∫ root (3){ cos^2 x} sin x dx `
\[\int\frac{\left( x + 1 \right) e^x}{\cos^2 \left( x e^x \right)} dx\]
` ∫ x {tan^{- 1} x^2}/{1 + x^4} dx`
\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]
\[\int \sin^4 x \cos^3 x \text{ dx }\]
\[\int \sin^5 x \text{ dx }\]
\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]
\[\int\frac{x^2}{x^2 + 6x + 12} \text{ dx }\]
\[\int\frac{2x + 1}{\sqrt{x^2 + 2x - 1}}\text{ dx }\]
\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]
\[\int\frac{1}{4 \cos x - 1} \text{ dx }\]
\[\int\frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} dx\]
\[\int x^2 e^{- x} \text{ dx }\]
\[\int\frac{\log \left( \log x \right)}{x} dx\]
\[\int\frac{\text{ log }\left( x + 2 \right)}{\left( x + 2 \right)^2} \text{ dx }\]
\[\int\frac{x + \sin x}{1 + \cos x} \text{ dx }\]
\[\int \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) \text{ dx }\]
\[\int \cos^3 \sqrt{x}\ dx\]
\[\int e^x \frac{\left( 1 - x \right)^2}{\left( 1 + x^2 \right)^2} \text{ dx }\]
\[\int\frac{e^x}{x}\left\{ \text{ x }\left( \log x \right)^2 + 2 \log x \right\} dx\]
\[\int x^2 \sqrt{a^6 - x^6} \text{ dx}\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x + 1 \right)^2} dx\]
\[\int\frac{1}{1 + x + x^2 + x^3} dx\]
\[\int\sqrt{\cot \text{θ} d } \text{ θ}\]
\[\int\frac{x^2 - 3x + 1}{x^4 + x^2 + 1} \text{ dx }\]
\[\int\frac{x}{\left( x - 3 \right) \sqrt{x + 1}} \text{ dx}\]
\[\int\frac{\sin^6 x}{\cos^8 x} dx =\]
\[\int\text{ cos x cos 2x cos 3x dx}\]
\[\int\frac{1}{4 \sin^2 x + 4 \sin x \cos x + 5 \cos^2 x} \text{ dx }\]
\[\int \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}} \text{ dx }\]
\[\int \left( \sin^{- 1} x \right)^3 dx\]
\[\int\frac{\cot x + \cot^3 x}{1 + \cot^3 x} \text{ dx}\]
Find : \[\int\frac{e^x}{\left( 2 + e^x \right)\left( 4 + e^{2x} \right)}dx.\]
