Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Advertisements
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
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^("a"x) cos"b"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)`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
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 (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
