M215 Project – The Area Function

Section 5.2 - 15 points

Due:

Recall that we can use the notation to denote the area under the curve f(t) between t = a and t = b.

1. Consider the constant function f(t) = 4.

a) Using geometry, compute

b) Similarly compute and

c) Using your answers to parts a) and b) as a guide, compute

d) We now define the area function

What is A(2)? A(2.5)? A(1)? Write a general formula for A(x).

2. Let

a) Using geometry, compute

b) Similarly, compute

c) Using your answers to parts a) and b) as a guide, compute

d) We now define another area function

What is B(2)? B(4)? B(0)? Write a general formula for B(x)?

e) We will now define a third area function

What is C(2)? C(4)? C(-1)? Write a general formula for C(x)?