Advertisements
Advertisements
Question
Integrate the following with respect to x:
x2 cos x
Advertisements
Solution
`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
RELATED QUESTIONS
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
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:
x sec x tan x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/(9x^2 - 4)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
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:
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 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
