# Thread: Quick check of my work? (Arc Length)

1. ## Quick check of my work? (Arc Length)

G'day! I'm supposed to set up integrals and evaluate the length of the curve for three problems. I just wanted to make sure I've got the set up done right, since evaluating should be relatively easy.

So, the formula I'm using is:

$\displaystyle \int_a^b{\sqrt{1+(f'(x))^2}}dx$

a) for the curve $\displaystyle y=e^xcosx$, in the interval $\displaystyle 0\leq{x}\leq{\pi}$

I got: $\displaystyle \int_0^{\pi}{\sqrt{1+e^{2x}(1-sin2x)}}dx$

b) for the curve: $\displaystyle y=2x+sinx$, in $\displaystyle 0\leq{x}\leq{4\pi}$

I got: $\displaystyle \int_0^{4\pi}{\sqrt{cos^2x+4cosx+5}}dx$

c) for the curve: $\displaystyle y=6x+cosx$, in $\displaystyle 0\leq{x}\leq{5\pi}$

I got: $\displaystyle \int_0^{5\pi}{\sqrt{cos^2x+12cosx+37}}dx$

Thank you very much, mates! Lemme know if you need the step in between!

2. a) is correct.

b) is correct.

c) should actually be $\displaystyle \displaystyle \int_0^{5\pi}{\sqrt{\sin^2{x} - 12\sin{x} + 37}\,dx}$.

3. Thanks, mate!

I wrote the wrong trigonometric function. It's not $\displaystyle cosx$, it's $\displaystyle sinx$!! It should read: $\displaystyle 6x + sinx$!

I wrote the wrong trigonometric function. It's not $\displaystyle cosx$, it's $\displaystyle sinx$!! It should read: $\displaystyle 6x + sinx$!
Yes, if the original function is $\displaystyle \displaystyle 6x + \sin{x}$ then your arc length integral is fine.