# estimate the integral

• December 15th 2009, 08:44 AM
Anonymous1
estimate the integral
Just got out of my Analysis final and one of the questions was:

Estimate $f(x) = \int_0^1 \sin(x^2)dx$ to within $10^{-3}.$

I may have gotten it right, but does anyone have any ideas?
• December 15th 2009, 09:23 AM
putnam120
I would probably have expanded $\sin (x^2)$ with a Taylor series and then integrated term by term (since the convergence is uniform). Though how many terms I am not quite sure.
• December 15th 2009, 10:57 AM
Anonymous1
That's what I did, only I'm not sure if my taylor expansion was right.
• December 15th 2009, 01:22 PM
Jester
Quote:

Originally Posted by Anonymous1
That's what I did, only I'm not sure if my taylor expansion was right.

$
\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} \pm \cdots
$
BTW - you only need two terms.