Explore and Discuss 1 (A) Which of the functions f ( x , y ) = 4 − x 2 − y 2 and g ( x, y ) = 4 − x − y would you guess has the greater average value over the rectangle R = { ( x , y ) | 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 } ? Explain. (B) Use double integrals to check the correctness of your guess in part (A).
Explore and Discuss 1 (A) Which of the functions f ( x , y ) = 4 − x 2 − y 2 and g ( x, y ) = 4 − x − y would you guess has the greater average value over the rectangle R = { ( x , y ) | 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 } ? Explain. (B) Use double integrals to check the correctness of your guess in part (A).
Solution Summary: The author explains how to guess the function which gives the greater average value by comparing with the given functions.
(A) Which of the functions f(x, y) = 4 − x2 − y2 and g(x, y) = 4 − x − y would you guess has the greater average value over the rectangle
R
=
{
(
x
,
y
)
|
0
≤
x
≤
1
,
0
≤
y
≤
1
}
? Explain.
(B) Use double integrals to check the correctness of your guess in part (A).
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
f(x), a piecewise function made up of a semicircle and 3 lines, is graphed in
the figure to the right. Arrange the following integrals from largest to
smallest.
I.
dx
II.
dx
II
Α.1 Π
В. П, І, Ш
С. П, Ш, I
D. II, І, I
Answer d please
Evaluate
+1+ x2
dx.
(1+ x²)²
Hint: Write this as two "easy" integrals. You do not need u-substitution or integration by-parts.
1
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences and Social Sciences Books a la Carte Edition Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY