antiderivative of (sin(x)^2)/x and its values

[Sendell]

I am given the function

(sin(x)^2)/x. The antiderivative is F(x). F(2) = .6, and I am asked what F(5) is.

Now, I have no idea how to approach finding the antiderivative of this function. I tried using the Wolfram Integrator, but I don't understand the answer it gave me. I don't think that finding the antiderivative is how I should start this problem.

Any ideas as to how to begin?

Thanks.

 

[skeeter]

first off ... is the function \(\displaystyle \L \frac{sin(x^2)}{x}\) or \(\displaystyle \L \frac{[sin(x)]^2}{x}\) ?

in any case, let's call it f(x). {small "f"}

\(\displaystyle \L F(5) - F(2) = \int_2^5 f(x) dx\)

so ...

\(\displaystyle \L F(5) = F(2) + \int_2^5 f(x) dx\)

you'll need a calculator to determine the value of the equation's right hand side to get F(5).

 

[Sendell]

Ingenious. Thank you!