Evaluate the integrals . underset(0)o...

Evaluate the integrals .
`underset(0)overset(pi//2)int (sin^(2)x-cos^(2)x)/(sin^(3)x+cos^(3)x)dx`

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Evaluate the integrals . int_(0)^(pi//2) (sin^(2)x-cos^(2)x)/(sin^(3)x+cos^(3)x)dx

Evaluate the following integrals (i) int_(0)^(pi/2) (sin^(2) x - cos^(2) x)/(sin^(3) x + cos^(3) x) dx

Knowledge Check

int ( sin^(3)x+cos^(3)x)/(sin^(2)x cos^(2)x)dx=

A

`sin x+cos x+c`

B

`tanx+cot x+c`

C

`secx-"cosec"x+c`

D

`sinx-cos x+c`

int_(0)^(pi//4) (sin^(2) x cos^(2) x)/((sin^(3) x + cos^(3)x)^(2))dx=

A

`1/3`

B

`1/6`

C

`1/2`

D

`1`

int (cos^(3)x + cos^(5) x)/(sin^(2)x + sin^(4) x) dx =

A

`sin x- 6 tan^(-1) (sin x) + c`

B

`sin x - 2(sin x)^(-1) + c`

C

`sin x- 2(sin x)^(-1) - 6tan^(-1) (sin x) + c`

D

`sin x - 2(sin x)^(-1) + 5tan^(-1) (sin x) + c`

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underset(0)overset(pi//2)(sin^(5)x)/(sin^(5)x+cos^(5)x) dx

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Find int_(0)^(pi//2) (sin^(5)x)/(sin^(5)x + cos^(5)x)dx

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int_(0)^(pi//2) (16sin x. cos x)/(sin^(4) x + cos^(4)x)dx=

AAKASH SERIES-DEFINITE INTEGRALS-Exercise-2.3 (Level-1)

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Evaluate the following integrals int(0)^((pi)/(2)) log(tan x)dx
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Evaluate the following integrals int(0)^(2pi) cos x dx
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Evaluate the following integrals (i) int(-1)^(1) log((2-x)/(2+x))dx
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int(-1)^(1)(x^(2) sin^(-1)x)/(sqrt(1-x^(2))dx
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int(-a)^(a) [sqrt(k+x+x^(2)) - sqrt(k-x+x^(2))]dx
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int(-(pi)/(2))^((pi)/(2))(sin^(2009)x + x^(1009))dx
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int(-(pi)/(2))^((pi)/(2)) (f(x) + f(-x))(g(x) - g(-x)) dx where f(x) a...
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Evaluate the following integrals (i) int(0)^(pi/2)(cos^(5//2)x)/(si...
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int(0)^((pi)/(2)) (1)/(1 + cot x)dx
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Evaluate the following integrals (iii) int(0)^(pi/2)(sqrt(sec x))/(s...
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int(0)^((pi)/(2))(4sqrt(cot x))/(4sqrt(tan x) + 4sqrt(cot x)) dx
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Evaluate the following integrals (i) int(0)^(pi/2)(2 sin x + 3 co...
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int(0)^((pi)/(2)) (3 tan x + 4 cot x)/(tan x + cot x)dx
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int(0)^((pi)/(2)) ("4 sec x + 5 cosec x")/("sec x + cosec x") dx
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int(0)^((pi)/(2)) (2 cos x-sinx)/(cos x + sin x)dx
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Evaluate underset(pi//6)overset(pi//3)int (sqrt(x))/(sqrt(sinx)+sqrt(c...
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int((pi)/(6))^((pi)/(3))(sec^(4)x)/("cosec"^(4) x + sec^(4)x) dx
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