1. p. 678
the x - axis

2. Area using n rectangles! How wide is each rectangle?
y = x2
How do we find each rectangle's height?
"too big" area =

3. Area using n rectangles!
y = x2
fundamental idea: to get the area, we . . . .
Or, we could just do . . . . .

4. Integral Notation and Areas
Area = rectangle 1 + rectangle 2 + . . . . + rectangle n
y = f (x)
x1 x2 x3
a b
One restriction: This works if, and only if, . . . . . .
n rectangles, each with width = ∆x
and height = f (xi)
a b

5. Find the area of the region bounded by y = x2 +1 and the x-axis from x = 1 to x = 3.
1) Using an integral by hand:
2) By graphing the curve on your grapher,
and looking at the 2nd Trace menu!
3) Using Math #9: fnInt on your calculator.

6. Find the area between each graph and the x-axis.
1) 2)
(why is the answer not area = ?)

8. Find the shaded area.
5) 6)
π
7)
a b

9. Homework
p. 679 2, 3, 7 "Use the Fundamental Theorem" means
p. 661 2 "use definite integrals and antiderivatives".
p. 647 1, 2
Next week: More applications of integrals.
Test: Monday, Nov. 21