Question

So, I'm doing Arc Length formula - I found the derivative of x^(3/2) = 9x/4, now I have sqrt(1+(9x/4)) - how do I rid of the sqrt without a perfect square?

Answer 1

i'm guessing you meant the derivative squared was 9x/4\[\Large \frac{ d }{ dx } x^{3/2} = \frac{ 3 x^{1/2} }{ 2 }\]
\[\Large \int\limits_{a}^{b} \sqrt{1 + \frac{ 9x }{ 4 }} dx\]use substitution -

let u=1+9x/4

Answer 2

du/dx = 9/4

Answer 3

\[4/9\int\limits_{4}^{5}\sqrt(U)du\]?

Answer 4

If I use a u-sub then I have to include the "du" - am I wrong?

Answer 5

That's all correct so far, good job. Just integrate it.

Answer 6

Webassign is super picky with it's answers, but I got it! thank you!

Answer 7

No prob.