Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
x3 sin x
Advertisements
उत्तर
`int x^3 sin x`
u = x3
u’ = 3x2
u” = 6x
u”’ = 6
u’v = 0
dv = sin x dx
⇒ v = `int sin x "d"x`
= – cosx
v1 = `int "v" "d"x`
= `int - cos x "d"x`
= `- int cos x "d"x`
= – sin x
v2 = `int "v"_1 "d"x`
= `int - sin x "d"x`
= `- int sin x "d"x`
= – (– cos x)
= cos x
v3 = `int "v"_2 "d"x`
= `int cos x "d"x`
= sin x
v4 = `int "v"_3 "d"x`
= `int sin x "d"x`
= – cos x
`int "u" "dv"` = uv – u’ v1 + u” v2 – u”’ v3 + u’vv4 – ………..
`int x^3 sin x "d"x = x^3 (- cos x) – 3x^2 (- sin x) + 6x (cos x) – 6 sin x + 0 (- cos x) + "c"`
= – x3 cos x + 3x2 sin x + 6x cos x – 6 sin x + c
APPEARS IN
संबंधित प्रश्न
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 :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x log x
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/(6x - 7 - x^2)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
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)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
