1. ## Estimate Integral

Estimate the integral with Trapezoidal rule: $\int_{-1}^2 x^2 dx$

$\Delta x = \frac{2 -(-1)}{4} = \frac{3}{4}$

$x = 0, y = 0; x=.75, y= .5625; x=1.5, y= 2.25; x=2.25, y=5.0625; x=3, y=9$

$T=\frac{\Delta x}{2}(y_0 + 2y_1 + 2y_2 + ... + 2y_{n-1} + y_n)$

$T = \frac{3}{8}\left(0 + 2(.5625) + 2(2.25) + 2(5.0625) + 9\right)$

$=9.75$

Now when I integrate this I get an answer of 3. Now what the heck is going on? My percent error is over 200%.I've done these problems a lot yet this one I keep getting way above the exact answer. Something is wrong here. What did I do wrong? It's driving me mad

2. Here yo = f(a) where a is -1.
y1 = f(a + Δx) = f(-1 + 0.75) = (-0.25)^2
and so on.
Now try to solve the problem.

3. Originally Posted by sa-ri-ga-ma
Here yo = f(a) where a is -1.
y1 = f(a + Δx) = f(-1 + 0.75) = (-0.25)^2
and so on.
Now try to solve the problem.
I don't quite understand what you are getting at here. The method I posted is the method that we've been doing these approximations. Find the change in x and then start from 0 and go up until your nth value is reached which in this case is 4. Then you just plug the x values into the function and get your y values. I've done several problems like this before and had no issues. For me to truly see what you are getting at here I'd need to see your full equation so I could compare it with my own.

Edit: WOW i am a complete idiot. I started at 0 when I should have started at -1 and gone to 2. This is unbelievable :|