Match the following items from List I into List II List -I List -II1∫sin2⁡xcos4⁡xdxAtan2⁡x2+ln⁡|cos⁡x|+c2∫sin4⁡xcos2⁡xdxBcos⁡x+sec⁡x+c3∫sin3⁡xcos2⁡xdxCtan3⁡x3+c4∫sin3⁡xcos3⁡xdxDtan⁡x+sin⁡2x4−3x2+c Ecos⁡x−sec⁡x+c

(1)=∫sin2⁡xcos4⁡xdx =∫tan2x sec2xdx=tan3⁡x3+c(2)∫sin4⁡xcos2⁡xdxUsing substitution method will get,tan⁡x+sin⁡2x4−3x2+c

Match the following items from List I into List II List -I List -II1∫sin2⁡xcos4⁡xdxAtan2⁡x2+ln⁡|cos⁡x|+c2∫sin4⁡xcos2⁡xdxBcos⁡x+sec⁡x+c3∫sin3⁡xcos2⁡xdxCtan3⁡x3+c4∫sin3⁡xcos3⁡xdxDtan⁡x+sin⁡2x4−3x2+c Ecos⁡x−sec⁡x+c

(1)=∫sin2⁡xcos4⁡xdx =∫tan2x sec2xdx=tan3⁡x3+c(2)∫sin4⁡xcos2⁡xdxUsing substitution method will get,tan⁡x+sin⁡2x4−3x2+c

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Match the following items from List I into List II

List -I List -II
1 $\int \frac{\sin^{2} x}{\cos^{4} x} d x$ A $\frac{\tan^{2} x}{2} + \ln | \cos x | + c$
2 $\int \frac{\sin^{4} x}{\cos^{2} x} d x$ B $\cos x + \sec x + c$
3 $\int \frac{\sin^{3} x}{\cos^{2} x} d x$ C $\frac{\tan^{3} x}{3} + c$
4 $\int \frac{\sin^{3} x}{\cos^{3} x} d x$ D $\tan x + \frac{\sin 2 x}{4} - \frac{3 x}{2} + c$
E $\cos x - \sec x + c$

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$1 - C, 2 - E, 3 - B, 4 - A$

$1 - C, 2 - D, 3 - B, 4 - A$

$1 - D, 2 - C, 3 - A, 4 - B$

$1 - C, 2 - E, 3 - A, 4 - D$

answer is B.

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Detailed Solution

(1)

$= \int \frac{\sin^{2} x}{\cos^{4} x} d x = \int \tan^{2} x s e c^{2} x d x$

$= \frac{\tan^{3} x}{3} + c$

(2) $\int \frac{\sin^{4} x}{\cos^{2} x} d x$

Using substitution method will get,

$\tan x + \frac{\sin 2 x}{4} - \frac{3 x}{2} + c$

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	List -I		List -II
1	$\int \frac{\sin^{2} x}{\cos^{4} x} d x$	A	$\frac{\tan^{2} x}{2} + \ln \| \cos x \| + c$
2	$\int \frac{\sin^{4} x}{\cos^{2} x} d x$	B	$\cos x + \sec x + c$
3	$\int \frac{\sin^{3} x}{\cos^{2} x} d x$	C	$\frac{\tan^{3} x}{3} + c$
4	$\int \frac{\sin^{3} x}{\cos^{3} x} d x$	D	$\tan x + \frac{\sin 2 x}{4} - \frac{3 x}{2} + c$
		E	$\cos x - \sec x + c$

Match the following items from List I into List II List -I List -II1∫sin2⁡xcos4⁡xdxAtan2⁡x2+ln⁡|cos⁡x|+c2∫sin4⁡xcos2⁡xdxBcos⁡x+sec⁡x+c3∫sin3⁡xcos2⁡xdxCtan3⁡x3+c4∫sin3⁡xcos3⁡xdxDtan⁡x+sin⁡2x4−3x2+c Ecos⁡x−sec⁡x+c

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