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Calculus and Beyond Homework Help
Solving a Line Integral Problem: Struggling for the Right Answer
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[QUOTE="galaxy_twirl, post: 4899505, member: 526444"] Hi everyone. I ran into a minor problem while trying to solve a problem on line integral. I suspect this question to be very straight-forward as it gave the parametric equations of the curve C. However, I am still unable to get the answer for some reason. May I have someone to point out where I went wrong? Thanks! Question: Ah, the image didn't get uploaded.. Please refer to the attached image. Thanks! The question in question is Q1(a). My attempt: Since x = t[SUP]2[/SUP] + 1 and y = t[SUP]3[/SUP]+t , we have x(t) and y(t). Following on, I went one to apply the formula, ∫ F⋅ d[B]r[/B] = ∫ f(x(t), y(t))||r'(t)|| dt. I had r(t) as (t[SUP]2[/SUP] + 1) [B]i [/B]+ (t[SUP]3[/SUP]+t) [B]j[/B]. And I have r'(t) = (2t) [B]i[/B] + (3t[SUP]2[/SUP] + 1) [B]j[/B], and ||r'(t)|| = √ (9t[SUP]2[/SUP] + 1)(t[SUP]2[/SUP] + 1). Since the range of t is 0 ≤ t ≤ 1, I integrated over this range and my calculator returned 3.73 as the answer, but the answer in my answer key wrote 6. May I know where I had gone wrong? Thanks! :D <In case the picture cannot be seen, I have uploaded it here.> Thanks again! [/QUOTE]
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Solving a Line Integral Problem: Struggling for the Right Answer
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