Question

Given the function f(x) = −2x, find the net signed area between f(x) and the x-axis over the interval [−4,9].

a) 90
b) 65
c) -90
d) -65

Answer 1

The net signed area between the function f(x) = -2x and the x-axis over the interval [-4,9] is -73.

Step-by-step explanation:

The net signed area between the function f(x) = -2x and the x-axis over the interval [-4,9] can be calculated using definite integration. Since the function is negative, the signed area will have a negative value. The definite integral of -2x over the given interval is:

-2 * ∫9-4 x dx

Using the power rule of integration, we get:

-2 * ([x^2/2] from -4 to 9)

= -2 * [(9^2/2) - (-4^2/2)]

= -2 * (81/2 - 8/2)

= -2 * (73/2)

= -73

Therefore, the net signed area between the function f(x) = -2x and the x-axis over the interval [-4,9] is -73.