Hey i have tried doing this problem and am having problem and the answer in the back of book is a number since its a definite integral bbut sofar I have integral of integral of ( 3 - 6sin(theta) 3 cos(theta) d(theta) )
#Trig substiiton using x =asina
cerulean fog
ember tapirBOT
cerulean fog
hold up ill try write i there
idk i def did something wrong because usually your meant to sub in 1-sin^2x
0but how do you do that with numbers infront
woven shuttle
Take 4 common and apply this formula
Then you can simply put the limits
Or if you want to derive it
Substitute x as 3/2sin(theta)
After taking 4 common
woven shuttle
U need to make the coeff of x^2 1
cerulean fog
wait
how does the 3/2 cancel
i get sqrt( 9 - 4(3/2sin(theta)^2 3/2cos(theta)d(theta)
woven shuttle
U need to take 4 common first
It will be 9/4 - 9/4 sin2(theta)
Take 4 out of the root
Out of the integral entirely
I'm prob sure there is derivation of this formula on the internet
fervent topaz
3(theta+cos(2theta)/2)+C
cerulean fog
no that was very wrong
ohh one question
is changing limits the same when doing u sub
just put in the limits into the x equation and use those?
or do you have to substitute in theta again
fervent topaz
11
there u go
sorry i was playing 2k lol
was doing mental math
this is easy stuff
use u substitution
fervent topaz
or do you have to substitute in theta again
you can do which ever one just make sure if you change your limits in terms of u stay in the u domain but if you dont unsub your u's back to x domain
or in this case theta domain instead of x
but this problem is a indifinite integral
fervent topaz
Hey i have tried doing this problem and am having problem and the answer in the...
use trig substitution on this one
fervent topaz
here u go
cerulean fog
use u substitution
oh nah this was the integral i was getting for the trig sub one lol i was terribly wrong
but right this makes sense thanks so much for writing it out
really appreciate it!
fervent topaz
Your welcome
cerulean fog
.solved