Problem

Find the value of integral C(z2+yx)ds, where C is parmeterized by r(t)=t,3t,t for 0t5

Answer

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Answer

Final Answer: 250113

Steps

Step 1 :Let the curve C be parameterized by r(t)=t,3t,t for 0t5

Step 2 :Compute the derivative of r(t) to get r(t)=1,3,1

Step 3 :Find the magnitude of r(t) to get ||r(t)||=11

Step 4 :Substitute r(t) into the function f(z,y,x)=z2+yx to get f(r(t))=2t2

Step 5 :Substitute f(r(t)) and ||r(t)|| into the integral to get 052t211dt

Step 6 :Compute the integral to get 250113

Step 7 :Final Answer: 250113

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