Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Advertisements
उत्तर
`int (1 + cos 4x)/(cos x - tan x) * "d"x = int (1 + cos 2(2x))/(cosx/sinx - sinx/cosx) * "d"x`
= `int (2cos^2 2x)/((sin^2x - cos^2x)/(sinx cos x)) * "d"x`
= `int (2sin x ocs x * cos^2 2x)/(cos^2x - sin^2x) * "d"x`
= `int (2sinx cosx * cos^2 2x)/(cos^2x - sin^2x) * "d"x`
= `int (sin 2x cos^2x)/(cos 2x) * "d"x`
= `int sin 2x cos 2x * "d"x`
= `int 1/2 xx 2 sin 2x cos 2x * "d"x` .......[sin 2A = 2 sin A cos A]
= `1/2 int sin 4x * "d"x`
= `1/2 xx - (cos 4x)/4 + "c"`
= `- 1/8 cos 4x + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Integrate the following functions with respect to x:
`sqrt(x^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 sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
