find the length of the curve y=x^(3/2) from x=0 to x=4

Question

anonymous · Answer

please someone help! I got 512/729 is that right?

terenzreignz · Answer

How?

anonymous · Answer

lol i did it over and got 8...

anonymous · Answer

$$\int\limits_{0}^{4}\sqrt{1+\frac{ 9x }{ 4 }}$$

anonymous · Answer

thats the equation. i know i got that part right its the algebra i keep making mistakes on

terenzreignz · Answer

You set up the definite integral correctly, but there's a bit of an error in how you evaluated it...

terenzreignz · Answer

$$\int\limits_{0}^4  \sqrt{1+\frac{9x}4} \ dx$$
So, I take it you took
$$\Large u = 1+\frac{9x}4$$$$\Large du = \frac94 dx$$

anonymous · Answer

yeah. after integrating i got $$\frac{ 8 }{ 27 } ( 1 + \frac{ 27x ^{\frac{ 3 }{ 2 }} }{ 8 }) $$

anonymous · Answer

after evaluating  everything in u to the 3/2 power.

terenzreignz · Answer

$$\frac49\int\limits_{1}^{10}  \sqrt{u} \ du$$

anonymous · Answer

whoah how did the inegral change from 0-4 to 1-10?

terenzreignz · Answer

Because that is u evaluated at the points x = 0 and x = 4

anonymous · Answer

can you please just do it out completely so i can see how you're getting that?

terenzreignz · Answer

I just replaced the 1+ (9x/4) with u
and the dx with the (4/9)du

anonymous · Answer

what do you get as an answer?

anonymous · Answer

whenever i do it i either get 8 or 512/729. the last one looks off cause that means it isnt even 1 unit long but 8 seems too big