Hi
I am having trouble trying to integrate this equation:
$\displaystyle \int \sqrt(1+2x+2x^3)$
how would i approach an expression like this?
Do i integrate the inside and then the outside?
P.S
Well, the original question asked to find the length of arc of $\displaystyle f(x) = \frac{2}{3}(1+x^2)^(\frac{3}{2})
$
$\displaystyle y=2-\frac{1}{2}x$ between x=0, y=3
I used the length of arc rule:
$\displaystyle \int_0^3 \sqrt{1+(2x(1+x^2)^{0.5})^2}dx$
This is where i was stuck:
$\displaystyle \int_0^3 \sqrt{1+2x+2x^3}dx$
Dear Paymemoney,
I have some problems regarding your question. You want to find the arc length of $\displaystyle f(x) = \frac{2}{3}(1+x^2)^{\frac{3}{2}}$ is'nt?
What is the second equation $\displaystyle y=2-\frac{1}{2}x$ ??? How did you get this? Do you want to find the arc length of this curve too??
Dear Paymemoney,
You have simplified incorrectly,
$\displaystyle \int_0^3 \sqrt{1+(2x(1+x^2)^{0.5})^2}dx$
$\displaystyle =\int_0^3\sqrt{1+4x^2(1+x^2)}dx$
$\displaystyle =\int_0^3\sqrt{1+4x^2+4x^4}dx$
$\displaystyle =\int_0^3\sqrt{(1+2x^2)^2}dx$
Can you continue from here??