Calculus BC Worksheet 35 Area Under A Curve 2

1-8: Find the area between the following curves and the x-axis

1. f(x) = x2 − 3x− 4 on [0, 4]

2. f(x) = cosx on [0, π]

3. f(x) = e−x on [−1, 2]

4. f(x) = 4− x2 on [0, 3]

5. f(x) = x2 − 4x− 3 on [0, 3]

6. f(x) = x2 − 5x+ 4 on [−1, 1]

7. f(x) = 2x− x2 on [0, 3]

8. f(x) = x2 − 4 on [−1, 3]

9. Find the area between x = y2 − 1 and the y-axis.

10. Find the area between y = x2 − 3 and y = 1.

11. Find the area between y2 = x and x+ y = 2.

12. Find the area between y =4

x2 + 4, the x-axis, and the lines x = −2 and x = 2.

13. Approximate to 3 decimal places the area under the curve y =√x on [0, 4] with 4 equal subintervals using:

(a) rectangles whose height is the right-hand endpoint

(b) rectangles whose height is the left-hand endpoint

(c) rectangles whose height is the midpoint of the subinterval, and

(d) trapezoids.

(e) Then evaluate the integral directly.

Answers:

1.56

32. 2 3.

e3 − 1

e2

4.23

35.

8

36.

26

3

7.8

38.

34

39.

4

3

10.32

311.

9

212. π

13a. 1 +√2 +√3 ≈ 4.146 13b. 3 +

√2 +√3 ≈ 6.146 13c.

√.5 +√1.5 +

√2.5 +

√3.5 ≈ 5.384

13d. 2 +√2 +√3 ≈ 5.146 13e.

16

3≈ 5.333