b. Write an integral to find the area under the curve.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Rational Functions And Conics
Section4.2: Graphs Of Rational Functions
Problem 88E
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I am looking to find the answer to 5b.

Refer to the region R in the first quadrant enclosed by the x-axis and the graph of the function
Refer to the region R in the first quadrant enclosed by the X-axis and the graph of the function
y = 4x – x3.
%3D
1. Find the locations where y = 4x – x intersects the xX-axis. Solve algebraically.
%3D
y=x(4-x²)
2
(x-2)=0 (xt2)=0
2. If R is partitioned into four subregions, each with a base of length Ax = -, what are the subintervals?
%3D
2'
Subinterval 2: LY2,]
r32,2]
Subinterval 1:
Subinterval 3: CI,27
15/8
Subinterval 4:
3. For each x-value listed in exercise 2, find the corresponding y-value.
9=400)-C0)3
15/3
y:H(2)-12)3
Point 1:
Point 2:
y:4-1=3
Point 3:
Point 4:
Point 5:O
=6-27/
4. Sketch the rectangles and compute (by hand) the area for each RAM with 4 subintervals. Tell whether
y:8-8
4= the method produces an overestimate or an underestimate.
5. Integration allows us to find the area enclosed by the x-axis and the curve.
a. If we were to find the area using integration, what would the lower and upper bounds of integration be?
Lower bound
2.
Upper bound
b. Write an integral to find the area under the curve.
c. What is the area under the curve using integration?
Mid Y
0.98 2.58 3.04 li64
a
Araa 0.25 0.6H 0.16 0,41=2,0625
2,0625u?
Transcribed Image Text:Refer to the region R in the first quadrant enclosed by the x-axis and the graph of the function Refer to the region R in the first quadrant enclosed by the X-axis and the graph of the function y = 4x – x3. %3D 1. Find the locations where y = 4x – x intersects the xX-axis. Solve algebraically. %3D y=x(4-x²) 2 (x-2)=0 (xt2)=0 2. If R is partitioned into four subregions, each with a base of length Ax = -, what are the subintervals? %3D 2' Subinterval 2: LY2,] r32,2] Subinterval 1: Subinterval 3: CI,27 15/8 Subinterval 4: 3. For each x-value listed in exercise 2, find the corresponding y-value. 9=400)-C0)3 15/3 y:H(2)-12)3 Point 1: Point 2: y:4-1=3 Point 3: Point 4: Point 5:O =6-27/ 4. Sketch the rectangles and compute (by hand) the area for each RAM with 4 subintervals. Tell whether y:8-8 4= the method produces an overestimate or an underestimate. 5. Integration allows us to find the area enclosed by the x-axis and the curve. a. If we were to find the area using integration, what would the lower and upper bounds of integration be? Lower bound 2. Upper bound b. Write an integral to find the area under the curve. c. What is the area under the curve using integration? Mid Y 0.98 2.58 3.04 li64 a Araa 0.25 0.6H 0.16 0,41=2,0625 2,0625u?
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