Advertisements
Advertisements
Question
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Advertisements
Solution
`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
RELATED QUESTIONS
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
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 :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
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 ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
