Find the exact area of each shaded region. The functions acting as the top boundaries are given.
8
6
4
2
1. f (x) = x2
-2
1
-1
2
3
4
5
4
3
2
1
2. f (x) = 2x + 1
0
0.5
1.0
1.5
2.0
2.5
3.0
1.0
0.8
0.6
0.4
0.2
3. f (x) = sin(x)
-1
1
2
3
4
3.0
2.5
2.0
1.5
4. f (x) = 2 + sin(x) (right boundary is at 2π)
5. f (x) = 4x − x2
2
4
6
2.0
1.5
1.0
0.5
6. f (x) = 1 +
√
x
-1
1
2
3
1
2
3
3.0
2.5
2.0
1.5
1.0
0.5
x
7. f (x) = e − x
2
-1
8. Top: f (x) = 20 − x2 . Bottom: g(x) = 2x + 12.
Answers: 1.
28
3
2. 4
3. 2
4. 4π
5.
32
3
6. approx 3.8856
3.722
7. approx 9.0557
8. 36