Question

Help with a confusing integral please?

Answer 1

\[\int\limits_{0}^{2\sqrt{3}}x^3(4-9x^2)^(1/2)\]

Answer 2

should be to the power of (1/2) or rad(4-9x^2)

Answer 3

the upper limit of integrations suggests a trig sub

Answer 4

I got the right integral but my question is how do I plug in 2rad3 back into it. the answer is -((4-9x^2)^(-3/2) * (27x^2+8)) / 1215

Answer 5

it becomes square rooting a negative number

Answer 6

When I did the trig sub x=(2/3)sin(theta) I couldn't change the limits of integration anyway since it doesn't fit into the range of sin

Answer 7

ok i lied no trig sub, go with
\[u=9-x^2\] should do it

Answer 8

I could see that working but if that still gives the same answer how do you plug in the limits of integration. I checked with wolfram. It would still be sqroot of a negative number

Answer 9

oooh so i see

Answer 10

wasn't paying attention
there is something wrong with the question

Answer 11

(64 (1 + 1079i * Sqrt[26]))/1215. Seems it doesn't have a real solution.

Answer 12

Hold on Slader.com had a solution to this question let me find it

Answer 13

They did u = 4-9x^2

And their answer was 64/1215 which seems to be rihgt

Answer 14

ohh their limits of integration changed to work out

Answer 15

love to see it
the domain is
\[[-\frac{2}{3},\frac{2}{3}]\] and \(2\sqrt3\) is not in it

Answer 16

They did:
\[\int\limits_{4}^{0}(1/9)(4-u)\sqrt{u}(-1/18)du\]

Answer 17

whatever they did, it cannot make any sense
the integrand is not defined on the most of the path of integration

Answer 18

That's really weird because my book said the answer was 64/1215

Answer 19

book is wrong

Answer 20

You mean the integral can't exist?

Answer 21

it is
\[f(x)=x^3\sqrt{4-9x^2}\] right?

Answer 22

Yes

Answer 23

Oh the graph is really interesting. only goes from -2/3 to 2/3 like you said

Answer 24

oh wait

Answer 25

the upper limit is 2/3 not 2rad3

Answer 26

Superfacepalm

Answer 27

My bad >.<

Answer 28

oh