Finding the value of the line integral $\frac25\int_{T} x \,\mathrm{d}s,$

Question

I have to find the value of the line integral

$$\frac25\int_{T} x \,\mathrm{d}s,$$

where the curve is the part of the "cutting curve" between the elliptical cylinder

$$\left(\frac{x}{20}\right)^2+\left(\frac{y}{5}\right)^2 = 1$$

and the planet $x = 4z$ in the first octant ($x\ge0, y\ge0, z\ge0$).

I have tried to solve this problem for some time now, and i cant figure out the correct way, and also, what is the right answer?

(Sorry for my english, it's not my native language)

Answer 1

HINT

• parametrize the line T by trigonometric functions $((x(t),y(t),z(t))\quad t\in [0,\pi/2]$
• set up and calculate the line integral $\frac25\int_{t_1}^{t_2} x(t)\sqrt{x'(t)^2+y'(t)^2+z'(t)^2}dt$