Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
x2 cos x
उत्तर
`int x^2 cos x "d"x`
u = x2
u' = 2x
u' = 2
u"' 0
dv = cos x dx
⇒ v= `int cos x "d"x`
= sin x
v1 = `int "v" "d"x`
= `int sinx "d"x`
= `- cos x`
v2 = `int "v"_1 "d"x`
= `int - cosx "d"x`
= `- sin x`
v3 = `int "v"_2 "d"x`
= `int- sin x "d"x`
= `- int sinx "d"x`
= `- (cos x)`
`int "u" "dv"` = uv – u'v1 + uv2 – u"'v3 + ...........
`int x^2 cos x "d"x = x^2 sin x - 2x xx cos x + 2 xx - sin x - 0 xx cos x + "c"`
`int x^2 cos x "d"x = x^2 sin x + 2x cosx - 2 sinx + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
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)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
