Can you help me with this question? The value of the integral of the function $g(x,y)=4x^3+10y^4$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $xy$-plane is?
My answer is coming $33\sqrt 5$. The correct answer is being shown as $33$ only. Need help?????
Your answer is correct. If $\gamma(t)=(t,2t)$, then that line integral is equal to$$\int_0^1g\bigl(\gamma(t)\bigr)\bigl\lVert\gamma'(t)\bigr\rVert\,\mathrm dt=\int_0^1(4t^3+160t^4)\sqrt5\,\mathrm dt=33\sqrt5.$$