Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Advertisements
उत्तर
`int (cos 2x)/(sin^2x cos^2x) "d"x = int (cos^2x - sin^2alpha)/(sin^2x cos^2x) "d"x`
= `int ((cos^2x)/(sin^2x cos^2x) - (sin^2x)/(sin^2x cos^2x)) "d"x`
= `int (1/(sin^2x) - 1/(cos^2x)) "d"x`
= `int ("cosec"^2x - sec^2x) "d"x`
= `int "cosec"^2x "d"x - int sec^2x "d"x`
= `- cot x - tan x + "c"`
= `- [cosx/sinx + sinx/cosx] + "c"`
= `-[(cos^2x + sin^2x)/(sinx cosx)] + "c"`
= `- 2/(sin 2x) + "c"`
= – 2 cosec 2x + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
