Advertisements
Advertisements
Question
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Advertisements
Solution
`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
RELATED QUESTIONS
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.
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve 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 (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
