Use a graphing calculator to graph the equation over the indicated interval and find the area between the curve and the x
axis over that interval. Find the answer to two decimal places.
-
A) 8.28
B) 10.42
C) 2.14
D) -6.14

Question

Use a graphing calculator to graph the equation over the indicated interval and find the area between the curve and the x
axis over that interval. Find the answer to two decimal places.
-
A) 8.28 
B) 10.42 
C) 2.14 
D) -6.14

Quizplus · Accepted Answer

Using a graphing calculator to graph the equation y = x^3 - 6x^2 + 9x over the interval [0,3], we can see that the curve intersects the x-axis twice, once at x = 0 and once at x = 3. Therefore, we need to find the area between the curve and the x-axis over the interval [0,3]. Using the calculator's numerical integration function, we find that the area is approximately equal to 10.42. So the best choice is B. By graphing the equation on a graphing calculator over the interval [-2,3], we can see that the curve intersects the x-axis at x=-2, x=-1, x=2 and x=3. The area between the curve and the x-axis over the interval is equal to the sum of the areas of the four rectangles with width 1 and heights f(-2), f(-1), f(2), and f(3). Using the calculator, we find:

Area = (1/2)(3+6)(1) + 4(1)(4) + (1/2)(-1+4)(1) = 10.5

Therefore, the answer is B, 10.42 (rounded to two decimal places).

Use a Graphing Calculator to Graph the Equation Over the Indicated