What is the antiderivative of xcos(x)??
2006-11-26 07:51:33 · 5 answers · asked by stutznut23 2 in Science & Mathematics ➔ Mathematics
use integration by parts:
u=x
dv= cos(x) dx
du =dx
v= sin(x)
integral of x cosx dx = xsinx - integral of sin(x) dx
= x sinx + cos(x) + C
[
2006-11-26 08:00:29 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Antiderivative = integration
so anitiderivative of xcosx =x sinx+sinx +c Ans.
2006-11-26 16:02:28 · answer #2 · answered by aminnyus 2 · 0⤊ 3⤋
He is wrong. Proof:
f(x)= -xsinx+cosx+c
f1(x) = -x(cosx) + -1(sinx) + (-sinx)
f1(x) = -xcosx -2sinx
right answer:
f(x)= xsinx + cosx + c
f1(x)= x (cosx) + 1(sinx) + (-sin x)
f1(x)= xcosx
Simply a change of negative.
2006-11-26 16:03:57 · answer #3 · answered by rjfink007 1 · 1⤊ 1⤋
u=x
dv= cos(x) dx
=>
du =dx
v= sin(x)
=>
integral ( x cosx ) dx = xsinx - integral ( sin(x) ) dx
= x sinx + cos(x) + C
.
2006-11-29 13:05:07 · answer #4 · answered by lobis3 5 · 1⤊ 0⤋
let cosx=dv and x=u
integrating by parts
x(-sinx)-int(-sinx) +C
=-xsinx+cosx+C
2006-11-26 15:54:11 · answer #5 · answered by raj 7 · 0⤊ 1⤋