Question

integrate cos(x/3) from 0 to pi using u substitution

Answer 1

u = x/3 ???

Answer 2

yep

Answer 3

du = (1/6)x^2

Answer 4

derivatives dont work like that ....

Answer 5

du = 1/3 dx

Answer 6

3du = dx

Answer 7

oh, I was trying to integrate

Answer 8

0 < x < pi

0/3 < x/3 < pi/3

0 < u < pi/3

Answer 9

@amistre64 is smart

Answer 10

integrate [0,pi] cos(x/3) dx

replace all the parts

integrate [0,pi/3] cos(u) 3 du

Answer 11

3sin(pi/3) - 3 sin(0)

Answer 12

im assuming you know how to integrate cos(u) of course

Answer 13

getting there

Answer 14

strategy; replace all x parts by u parts

Answer 15

how is that step written, without the upper and lower bounds?

Answer 16

we have the upper and lower bounds, so im not sur what you mean

Answer 17

after we choose the substitution, find its derivative, then the next step looks like what...to me, it doesn't make sense to put the upper and lower bounds on it...am I wrong?

Answer 18

the bounds on x are:

0 < x < pi

right?

but u = x/3, or 3u = x

0 < 3u < pi ; solve for u, divide off the 3

0 < u < pi/3

Answer 19

we now have the bounds in terms of u

Answer 20

ok...processing

Answer 21

\[3\int\limits_{0}^{\pi/3}\cos(u)du\]

Answer 22

yeah

Answer 23

ok, now I integrate that using indefinite...then subtract upper bounds from lower bounds

Answer 24

yeah, integration hasnt changed ... the key here is in converting all the x parts to u parts.

Answer 25

gotcha

Answer 26

how is this next step written

Answer 27

its integration, youve already covered that before you delve into subsitutions ...

Answer 28

youve even mentioned how to work it ....

Answer 29

and its a definite integral, its defined by the boundarys.

indefinite has no bounds

Answer 30

so, do I just write 3sin(u)?

Answer 31

almost, plug in your bounds ....

Answer 32

you get a value, not a function ....

Answer 33

right, I shouldn't write that last part by itself

Answer 34

3sin(u) [evaluated at: 0 and pi/3]

and ive already posted above what it looks like ....

Answer 35

ok, processing

Answer 36

(3(sqrt(3))/2

Answer 37

\[(3\sqrt(3))/2\]

Answer 38

yep

Answer 39

woot

Answer 40

thanks all

Answer 41

yw