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
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Find the integrals of the following:
`1/(9x^2 - 4)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
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 sin^2x "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
