Expert: Paul Klarreich - 3/10/2010

Question
hi

i've some problems to solve this integral

x^3sqrt(4 -x^2)dx

i should solve it using trigonometric sub.

this what i did

x=2sin@
dx=2cosd@

2*(2sin@)^3*cos^2@ d@

then i integrated but i don't get the right answer =(

your help is very much appreciated

Answer
Questioner: meme
Country: Qatar
Category: Calculus
Private: No
Subject: cal II
Question: hi

i've some problems to solve this integral

x^3sqrt(4 -x^2)dx

i should solve it using trigonometric sub.

this what i did

x = 2 sin t
dx=2 cos t dt    << don't get careless.

2*(2sin t )^3*cos^2 t  dt


>>> I think you lost a '2' here.



x^3sqrt(4 -x^2)dx =

================ NOTATION ==========================
I will write   s = sin t,  c = cos t, to save typing.
====================================================

(2s)^3(2c)(2 c) dt =

32 s^3 c^2 dt =

Now write  s^3 = s(1 - c^2)

32 s(1 - c^2) c^2 dt

Now dc = - s dt and:

- 32 (1 - c^2) c^2 dc

and the rest of it should go easily:

................................................
then i integrated but i don't get the right answer =(

your help is very much appreciated