a direction field is drawn for the given equation. Sketch some integral curves. 0.8y0.60.40.20-0.2--0.4-0.6--0.8-100.20.41.41.61.8210.60.811.2Figure 1.3E.4: A direction field for y'=1+x²+y2

Step 1:Integral curves are drawn along the direction of the field as shown in the image below:

Answered: 0.8 y 0.6 0.4 0.2 0 -0.2- -0.4 -0.6-…

0.8 y 0.6 0.4 0.2 0 -0.2- -0.4 -0.6- -0.8 -1 0 0.2 0.4 1.4 1.6 1.8 2 1 0.6 0.8 1 1.2 Figure 1.3E.4: A direction field for y' = 1+x²+y2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question

a direction field is drawn for the given equation. Sketch some integral curves.

0.8
y
0.6
0.4
0.2
0
-0.2-
-0.4
-0.6-
-0.8
-1
0
0.2
0.4
1.4
1.6
1.8
2
1
0.6
0.8
1
1.2
Figure 1.3E.4: A direction field for y'
=
1+x²+y2

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.

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