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Step 5 Thus, we have found the line integral. a/2 56 sin (t) cos(t) dt = 5E 2.5 -n/2 6250

Step 5 Thus, we have found the line integral. a/2 56 sin (t) cos(t) dt = 5E 2.5 -n/2 6250

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 20T
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Evaluate the line integral, where C is the given curve. xy ds, C is the right half of the circle x2 + y2 = 25 oriented counterclockwise Step 1 The parametric equations for the circle x2 + y? = 25 are as follows. X = 5 cos(t) y = sin(t) Step 2 Since we want only the right half of the circle, then t has the following limits. (Choose angle values between -n and n). sts Step 3 From the text, we know the following formula. V - ( ds = (-5 sin(t))? + (5 cos(t) dt = V 25(sin?(t) + cos?(t)) dt. Remembering that sin2(0) + cos²(0) = 1 we have ds = dt. Step 4 Now we have the following. xy4 ds = (5 cos(t))(5 sin(t))“(5 dt) - T/2 sin (t) cos(t) dt Step 5 Thus, we have found the line integral. 56 sin (t) cos(t) dt = -1/2 -(( 2.5 = 6250 -n/2
Transcribed Image Text:Evaluate the line integral, where C is the given curve. xy ds, C is the right half of the circle x2 + y2 = 25 oriented counterclockwise Step 1 The parametric equations for the circle x2 + y? = 25 are as follows. X = 5 cos(t) y = sin(t) Step 2 Since we want only the right half of the circle, then t has the following limits. (Choose angle values between -n and n). sts Step 3 From the text, we know the following formula. V - ( ds = (-5 sin(t))? + (5 cos(t) dt = V 25(sin?(t) + cos?(t)) dt. Remembering that sin2(0) + cos²(0) = 1 we have ds = dt. Step 4 Now we have the following. xy4 ds = (5 cos(t))(5 sin(t))“(5 dt) - T/2 sin (t) cos(t) dt Step 5 Thus, we have found the line integral. 56 sin (t) cos(t) dt = -1/2 -(( 2.5 = 6250 -n/2
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