Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
9xe3x
Advertisements
उत्तर
`int 9x"e"^(3x) "d"x = 9 int x"e"^(3x) "d"x`
`int "u" "dv" = "uv" - "u'v"_1 + "u''v"_2 - "u""'''""v"_3 + "u""''""v"_4 -` ...........(1)
u = x
u' = 1
u = 0
dv = `"e"^(3x) * "d"x`
v = `int "e"^(3x) * "d"x`
= `("e"^(3x))/3`
v1 = `int "v" "d"x`
= `int ("e"^(3x))/3 * "d"x`
= `1/3 xx 1/3 "e"^(3x)`
v2 = `int "v"_1 "d"x`
= `int 1/3^2 "e"^(3x) * "d"x`
= `1/3^2 xx 1/3 "e"^(3x)`
`9int x "e"^(3x) "d"x = 9[x ("e"^(3x))/3 - 1 xx 1/3^2 "e"^(3x) + 0 xx 1/3^2 "e"^(3x)]`
`9int x "e"^(3x) "d"x = 9[x/3 "e"^(3x) - 1/3^2 "e"^(3x)]`
`9int x "e"^(3x) "d"x = (3x - 1) "e"^(3x) + "c"`
APPEARS IN
संबंधित प्रश्न
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`
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
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:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
