Question: Evaluate the line integral, where C is the given curve.Cxy4 ds, Cis the right half of the circle x2+ y2=25 oriented counterclockwiseStep 1The parametric equations
Evaluate the line integral, where C is the given curve.Cxy4 ds, Cis the right half of the circle x2+ y2=25 oriented counterclockwiseStep 1The parametric equations for the circlex2+ y2=25are as follows.x=55cos(t)y=55sin(t)Step 2Since we want only the right half of the circle, then t has the following limits.(Choose angle values between and ).$$2 t $$2Step 3From the text, we know the following formula.ds=dxdt2+dydt2=(5 sin(t))2+5$$cos(t)2dt=25(sin2(t)+ cos2(t))dt.Remembering thatsin2()+ cos2()=11,we haveds =55dt.Step 4Now we have the following.xy4 dsC=/2(5 cos(t))(5 sin(t))4(5 dt)/2=/25 sin (t) cos(t) dt/2
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