Determine whether the following statements are true and give an explanation or counterexample.

a. Suppose that f is a positive decreasing function, for x > 0. Then the area functionis an increasing function of x.

b. Suppose that f is a negative increasing function, for x > 0. Then the area functionis a decreasing function of x.

c. The functions p(x) = sin 3x and q(x) = 4 sin 3x are antiderivatives of the same function.

d. If A(x) = 3x² - x - 3 is an area function for f, then B(x) = 3x² - x is also an area function for f.

e. 

Transcribed Image Text:

= SF(1) di A(x) A(x) = S°F(t) di - Söf(t) dt