AP Calculus AB - Worksheet 55
Exact Area Under a Curve w/ Notes
Steps for finding the Area Under a Curve
-
Graph
-
Shade the region enclosed by
region, so you must include the x-axis (y = 0)
-
As long as the entire shaded region is above the x-axis then
Examples:
1)
2)
3)
4)
Make graphing easy!! Find the x-intercepts:
5)
You can only take the area of a closed
Worksheet 55
Exact Area Under a Curve
Problems #1 – 8: Graph and find the area under the graph of
1.
2.
3.
4.
5.
6.
7.
8.
from a to b by integrating.
For #9 – 10: Graph and find the area of the region bounded by
and the x-axis.
In these two problems, you need to “find” a (left most x-value) and b (right most x-value). They are
where
crosses the x-axis.
9. Bounded by the x-axis and the parabola
10. Bounded by the x-axis and the parabola
(What is a?
(What is a?
b?
)
b?
)
For #11: Graph the region stated and then find the area of the bounded region.
11. Bounded by the curve
Answers:
15
1.
2
5. 2
9. a = 2; b = −2
32
3
and the lines
21
2
3 −1
6.
2
10. a = 0; b = 4
32
3
2.
and
(What is a?
32
3
e2 − 1
7.
2
11. a = 0; b = 4
16
3
3.
b?
)
32
3
e2 − 1
8.
e
4.