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

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: