sy = sin(x)- y = cos(x) T/2 Two students, S and T, considered this problem: Consider the region trapped between the graphs of y = sin x and y = cos x, on the interval 0 < x < 5. This region is shaded in the figure included above. To find the area of the shaded region, Student S set up the following integral. SF (sin z – cos æ) dæ However, Student T says this won't find the correct value. What do you think? Student T is correct. A better integral expression is SF (cos x – sin æ) dr Student T is incorrect. Student S has set up the integral correctly. Student T is correct. A better integral expression is S* (sin æ – cos æ) dx + ƒ? (cos ¤ – sin æ) dx Student Tis correct. Student S should include Tr² like this: TS3 (sin æ – cos æ)² dæ

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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y= sin(x)
y = cos(x)
TT/2
ST/2
Two students, S and T, considered this problem:
Consider the region trapped between the graphs of y = sin x and y = cos x, on the interval 0 < x < .
This region is shaded in the figure included above.
To find the area of the shaded region, Student S set up the following integral.
S (sin æ – cos æ) dx
However, Student T says this won't find the correct value.
What do you think?
Student T is correct. A better integral expression is
L² (cos x – sin x) dæ
Student T is incorrect.
Student S has set up the integral correctly.
Student T is correct. A better integral expression is
L* (sin x – cos x) dx + f7 (cos x – sin æ) dx
Student T is correct. Student S should include Tr² like this:
T7 (sin x – cos T)
- cos r)°dx
Transcribed Image Text:y= sin(x) y = cos(x) TT/2 ST/2 Two students, S and T, considered this problem: Consider the region trapped between the graphs of y = sin x and y = cos x, on the interval 0 < x < . This region is shaded in the figure included above. To find the area of the shaded region, Student S set up the following integral. S (sin æ – cos æ) dx However, Student T says this won't find the correct value. What do you think? Student T is correct. A better integral expression is L² (cos x – sin x) dæ Student T is incorrect. Student S has set up the integral correctly. Student T is correct. A better integral expression is L* (sin x – cos x) dx + f7 (cos x – sin æ) dx Student T is correct. Student S should include Tr² like this: T7 (sin x – cos T) - cos r)°dx
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