Advertisements
Advertisements
प्रश्न
\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
विकल्प
- \[\frac{1}{3} \tan^2 x + C\]
- \[\frac{1}{2} \tan^2 x + C\]
- \[\frac{1}{3} \tan^3 x + C\]
none of these
MCQ
उत्तर
\[\frac{1}{3} \tan^3 x + C\]
\[\text{Let }I = \int\frac{\sin^2 x dx}{\cos^4 x}\]
\[ = \int\frac{\sin^2 x}{\cos^2 x} \times \frac{1}{\cos^2 x}dx\]
\[ = \int \tan^2 x \cdot \sec^2 x dx\]
\[\text{Let }\tan x = t\]
\[ \Rightarrow \sec^2 x dx = dt\]
\[ \therefore I = \int t^2 \cdot dt\]
\[ = \frac{t^3}{3} + C\]
\[ = \frac{\tan^3 x}{3} + C ..........\left( \because t = \tan x \right)\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
If f' (x) = 8x3 − 2x, f(2) = 8, find f(x)
\[\int \sin^2 \frac{x}{2} dx\]
` ∫ sin 4x cos 7x dx `
\[\int\frac{\cos 4x - \cos 2x}{\sin 4x - \sin 2x} dx\]
\[\int\frac{\sin 2x}{a^2 + b^2 \sin^2 x} dx\]
\[\int\frac{x + 1}{x \left( x + \log x \right)} dx\]
\[\int\frac{1 + \cot x}{x + \log \sin x} dx\]
\[\int\frac{\left( x + 1 \right) e^x}{\cos^2 \left( x e^x \right)} dx\]
\[\int2x \sec^3 \left( x^2 + 3 \right) \tan \left( x^2 + 3 \right) dx\]
\[\int\frac{x^2 + 3x + 1}{\left( x + 1 \right)^2} dx\]
\[\int \sin^3 x \cos^6 x \text{ dx }\]
\[\int \sin^7 x \text{ dx }\]
\[\int\frac{1}{\sqrt{a^2 + b^2 x^2}} dx\]
` ∫ { x^2 dx}/{x^6 - a^6} dx `
\[\int\frac{1}{\sqrt{5 - 4x - 2 x^2}} dx\]
\[\int\frac{x}{\sqrt{4 - x^4}} dx\]
\[\int\frac{\sin 8x}{\sqrt{9 + \sin^4 4x}} dx\]
\[\int\frac{x^2}{x^2 + 7x + 10} dx\]
\[\int\frac{x + 1}{\sqrt{4 + 5x - x^2}} \text{ dx }\]
\[\int\frac{2x + 5}{\sqrt{x^2 + 2x + 5}} dx\]
\[\int\frac{1}{1 - 2 \sin x} \text{ dx }\]
\[\int x^2 \text{ cos x dx }\]
\[\int \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}} dx\]
\[\int e^x \left( \frac{1 + \sin x}{1 + \cos x} \right) dx\]
\[\int e^x \sec x \left( 1 + \tan x \right) dx\]
\[\int\sqrt{3 - x^2} \text{ dx}\]
\[\int\frac{\sin 2x}{\left( 1 + \sin x \right) \left( 2 + \sin x \right)} dx\]
\[\int\frac{x^2 + 1}{\left( 2x + 1 \right) \left( x^2 - 1 \right)} dx\]
\[\int\frac{x^2}{\left( x - 1 \right) \left( x + 1 \right)^2} dx\]
\[\int\frac{3}{\left( 1 - x \right) \left( 1 + x^2 \right)} dx\]
\[\int\frac{x^2 + 9}{x^4 + 81} \text{ dx }\]
\[\int\frac{1}{x^4 + 3 x^2 + 1} \text{ dx }\]
\[\int e^x \left( 1 - \cot x + \cot^2 x \right) dx =\]
\[\int \sec^2 x \cos^2 2x \text{ dx }\]
\[\int \cot^5 x\ dx\]
\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]
\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]
\[\int\frac{1}{\sec x + cosec x}\text{ dx }\]
\[\int\sqrt{a^2 + x^2} \text{ dx }\]
\[\int\sqrt{a^2 - x^2}\text{ dx }\]
