# antiderivative question - help

• Jan 18th 2010, 07:54 PM
Baatata
antiderivative question - help
http://img64.imageshack.us/img64/5430/80433637.jpg

for
a. i get:
local max: 2.5*pi
local min: 1.5*pi

b. global max: 3.5pi
global min: 2pi/3

are a and b right?

c. how to do this?

d. by the fundamental theorem of calculas (for this question) g'(x)=f(x) so i will have to find the antiderivative of g'(x).. but whats the antiderivative of xsinx? i dont know how to get it..
• Jan 18th 2010, 08:06 PM
pickslides
Quote:

Originally Posted by Baatata
but whats the antiderivative of xsinx? i dont know how to get it..

you need to employ integration by parts which says

$\displaystyle \int uv' = uv - \int vu'$

in your case make $\displaystyle u = x$ and $\displaystyle v' = \sin(x)$
• Jan 18th 2010, 08:23 PM
VonNemo19
Quote:

Originally Posted by Baatata
http://img64.imageshack.us/img64/5430/80433637.jpg

for
a. i get:
local max: 2.5*pi
local min: 1.5*pi

b. global max: 3.5pi
global min: 2pi/3

are a and b right?

c. how to do this?

d. by the fundamental theorem of calculas (for this question) g'(x)=f(x) so i will have to find the antiderivative of g'(x).. but whats the antiderivative of xsinx? i dont know how to get it..

It seems to me that $\displaystyle \int_0^xf(t)dt=\int_0^xt\sin{t}dt$ and by parts we have

$\displaystyle g(x)=\int_0^xt\sin{t}dt=-t\cos{t}\Big|_0^x+\int_0^x\cos{t}dt$. So, now employ the FTC.
• Jan 18th 2010, 08:30 PM
Baatata
could you guys break it down for me? i have no idea what you did there.. (Surprised)
• Jan 18th 2010, 08:34 PM
pickslides
$\displaystyle \int uv' = uv - \int vu'$

in your case make $\displaystyle u = x$ and $\displaystyle v' = \sin(x)$

Go and find

$\displaystyle v = \int \sin(x)$ and $\displaystyle u' = \frac{d}{dx}~x$

Sub these into

$\displaystyle \int uv' = uv - \int vu'$

....

Vonnemo has given you the answer to this in his response.
• Jan 18th 2010, 08:45 PM
Baatata
i kinda get it even though i cant figure out how u came up with this forumla

but anyways.. back to the original question, once i found the antiderivative, what do i have to do next?
• Jan 18th 2010, 08:56 PM
pickslides
Quote:

Originally Posted by Baatata
i kinda get it even though i cant figure out how u came up with this forumla

This formula comes from the product rule of differentiation.

Recall

$\displaystyle (uv)' = uv'+vu'$

If you integrate both sides of this equation you get the formula I gave you.

Quote:

Originally Posted by Baatata

but anyways.. back to the original question, once i found the antiderivative, what do i have to do next?

You sub in the terminals
• Jan 19th 2010, 08:10 PM
Baatata
well i just had some help from my friend and he said that i dont even need g(x).

so g'(x) = xsinx.
g'(x) = 0 when x=0,pi, 2pi, 3pi, 4pi
how do i figure out which on is local min/max and global min/max?
i know that when it changes from + to - its local max but what about global max? when would that be?