Evaluate the line integral, where C is the given curve.

Question

(Integral)C z dx + x dy + y dz,
C: x = t^4, y = t^5, z = t^4, 0 ≤ t ≤ 1

Answer 1

Just plug and chug

∫_Cz dx + x dy + y dz
= ∫[0,1] (t^4)(4t^3) + (t^4)(5t^4) + (t^5)(4t^3) dt
= ∫[0,1] 4t^7 + 9t^8 dt
= 1/2 t^8 + t^9 [0,1]
= 1/2 + 1
= 3/2