Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
उत्तर
`int "e"^("a"x) sin "b"x "d"x = "e"^("a"x)/("a"^2 + "b"^2) ["a" sin "b"x - "b" cos "b"x] + "c"`
Here a = – 4, b = 2
`int "e"^(- 4x) sin 2x "d"x = "e"^(- 4x)/((- 4)^2 + 2^2) [-4 sin 2x - 2 cos 2x] + "c"`
`int "e"^(- 4x) sin 2x "d"x = "e"^(- 4x)/(16 + 4) [- 4 sin 2x - 2 cos 2x] + "c"`
`int "e"^(- 4x) sin 2x "d"x = - "e"^(- 4x)/20 xx 2[2 sin 2x + cos 2x] + "c"`
`int "e"^(- 4x) sin 2x "d"x = - "e"^(- 4x)/10 [2 sin 2x + cos 2x] + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
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 sec x tan x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
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 ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
