Calculus 3 Quiz
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VECTOR FIELDS & LINE/SURFACE INTEGRALS
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Consider two curves: C1C_1 is the straight line from (0,0,0)(0,0,0) to (1,1,1)(1,1,1), and C2C_2 is the curve parameterized by r(t)=(t,t2,t3)\mathbf{r}(t) = (t, t^2, t^3) for 0≤t≤10 \leq t \leq 1. Both curves connect the same endpoints. If f(x,y,z)=x2+y2+z2f(x,y,z) = x^2 + y^2 + z^2, which statement about the line integrals ∫C1f ds\int_{C_1} f \, ds and ∫C2f ds\int_{C_2} f \, ds is correct?
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