this is not a simple plane curve or a close plane curve so I use the formula:
∫ F ⋅ dr/dt dt
The Attempt at a Solution
From the point (0,0) to (2,4)
Direction Vector v(t) = <2-0, 4-0>
r(t) = (2t + 0) i + (4t + 0) j
r'(t) = 2i + 4j
∴ F(x(t),y(t)) = (4t)2i + 2(2t)(4t)j = (16t2)i + (16t2)j
F(x(t),y(t)) ⋅ r'(t) =( (16t2)i + (16t2)j ) ⋅ (2i + 4j) = 32t2 + 64t2
I feel my math is correct which leads me to believe my approach is incorrect. The final answer is supposed to be 32 evaluated from 0 to 2.
But if I finished my integral : ∫ 96t2dt = 32t3
Can someone please help me.
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