Use the fundamental theorem of calculus to find the area of the region between the graph of the function x^5 + 8x^4 + 2x^2 + 5x + 15 and the x-axis on the interval [-6,6]. Round off your answer to the nearest integer. A) 25,351 units^2
B) 149,473 units^2
C) 3,758 units^2
D) 2,362 units^2

The area of the region is 25,351 .

Step-by-step explanation:

The Fundamental Theorem of Calculus: if is a continuous function on , then

where is an antiderivative of .

A function is an antiderivative of the function if

The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.

To find the area of the region between the graph of the function and the x-axis on the interval [-6, 6] you must:

Apply the Fundamental Theorem of Calculus