Page 97 - Calc for the Clueless

Another method is to approximate the region using parabolas on the top. We will isolate one of these regions.
As you will see, only if n = even, an even number of intervals, will this method work.

Let the parabola be given by y = f(x) = ax + bx + c.
2
2
y at the left end is y L = f(-h) = ah - bh + c
y in the middle is y M = f(0) = c

y at the right is y R = f(h) = ah + bh + c
2
The area of this region is

Do something "weird." Factor out h/3 because it works!!

Just like before, the lower base of the first region is the upper base of the second region. Four times the middle
never changes.

The formula issss... A = h/3(y 0 + 4y 1 + 2y 2 + 4y 3 + ... + 4y n-1 + y n), n even.

Example 10—

Note
The real cones above and the parabola and hyperbola are not twncated, but go on forever and
ever.

Let's do the same example.

Approximate