Give an example of a function that is continuous on the interval (0,5). Then graph the function using a table, find its antiderivative, and find the definite integral using (0,5) as the endpoints.

Answer 1

ok

y = 2 is continuous on (0,5)

x y

0+ 2

1 2

2 2

3 2

4 2

5- 2

the anti-derivative is F(x) = 2x+c but the constant of integration will cancel out eventually, so forget about it

the area under the curve is F(5) - F(0) = 2*5 - 2*0 = 10

is a rectangle 2 by 5