Question

having trouble trying to integrate sqrt (900-300(t)sqrt 2+100t^2) from 0 to 3sqrt 2

Answer 1

does that sqrt go over the whole thing?

Answer 2

ya.

Answer 3

k give me a sec let me think

Answer 4

do you know trig substitution?

Answer 5

ya but was having trouble tring to find the right thing to plug in

Answer 6

=int(sqrt(100)*sqrt(t^2-3sqrt(2)t+9)
=int(10*sqrt(t^2-3sqrt(2)t+9/2+9-9/2)
=int(10*sqrt([t-3sqrt(2)/2)]^2+9/2)
let tan pheta=[t-3sqrt(2)/2]/[3/sqrt(2)]
{3/sqrt(2)} *tan pheta=t-3sqrt(2)/2

Answer 7

{3/sqrt(2)}*sec^2(pheta) d(pheta)=dt
so we have
=int(10*(sqrt([9/2]tanpheta+9/2)*[3/sqrt(2)*sec^2pheta)

Answer 8

10int(sqrt(9/2)*sqrt(tanpheta+1)*[3/(sqrt(2))]sec^2pheta)
=10(3/sqrt(2))(3/sqrt(2))int(sqrt(sec^2pheta)sec^2pheta)
=10(9/2)int(secpheta*sec^2pheta)
=45int(sec^3pheta)

Answer 9

is this helpful?

Answer 10

very helpful

Answer 11

should i go further? i havent done anything with the limits yet

Answer 12

na i can do the limits

Answer 13

k cool have fun

Answer 14

thx for the help

Answer 15

i had to complete the square above just so you know