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Learn Exercise 7.3 with Free Lessons & Tips

Find the integrals of the functions

 

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Find the integrals of the functions

 =  

 =  = 

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Find the integrals of the functions

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Find the integrals of the functions

It is known that, 

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Find the integrals of the functions

cos 2x cos 4x cos 6x

It is known that,

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Find the integrals of the functions

sin3 (2x + 1)

Let 

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Find the integrals of the functions 

 sin3x cos3x

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Find the integrals of the functions

 
sin x sin 2x sin 3x

It is known that, 

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Find the integrals of the functions

 
sin 4x sin 8x

GIVEN function is integral of (sin4x*sin8x).dx

 

we know:- sinAsinB = 1/2[cos(A-B)-cos(A+B)]

 

NOW, \sf{\int{sin4x*sin8x}\,dx}

 

=\sf{\int{1/2[cos(-4x)-cos(12x)]}\,dx}

 

=\sf{\int{1/2[cos4x-cos12x]}\,dx}

 

=\sf{1/2[\frac{sin4x}{4}-\frac{sin12x}{12}]+c}

 

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Find the integrals of the functions

 

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Find the integrals of the functions

sin4x

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Find the integrals of the functions

cos4 2x

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Find the integrals of the functions

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Find the integrals of the functions

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Find the integrals of the functions

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Find the integrals of the functions

 

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Find the integrals of the functions

tan4x

From equation (1), we obtain

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Find the integrals of the functions 

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Find the integrals of the functions 

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Find the integrals of the functions

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Find the integrals of the functions

sin−1 (cos x)

It is known that,

Substituting in equation (1), we obtain

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Find the integrals of the functions

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 is equal to

A. tan x + cot x + C

B. tan x + cosec x + C

C. − tan x + cot x + C

D. tan x + sec x + C

Hence, the correct answer is A.

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 equals

A. âˆ’ cot (exx) + C

B. tan (xex) + C

C. tan (ex) + C

D. cot (ex) + C

Let exx = t

Hence, the correct answer is B.

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