Ive got an interesting question:
Without computing any integral, show that: $\int_{\vec{b}(t)}(x^{10}$i$+y^{10}$j$)· d\vec{b} = 0$
where $\vec{b}(t)=\sqrt{3}t^2$i$+(t^3-t)$j when $− 1 ≤ t ≤ 1$
This line integral question has stumped me. How am I meant to prove it without computing any integrals? Any help will be appreciated.