Find $\int_{C} x^{5} y^{2} d x$ where $C$ is the arc of the curve $x=y^{2}$ from $(0,0)$ to $(4,2)$. Question Help: iㅣㅂ vIDEO D Post to forum

Step 1 ：Parameterize the curve C using the equation \(x=y^{2}\), where \(y\) ranges from 0 to 2.

Step 2 ：Substitute \(x\) with \(y^{2}\) in the integrand to get \(y^{12}\).

Step 3 ：Integrate \(y^{12}\) with respect to \(y\) from 0 to 2 to get the integral.

Step 4 ：The integral of \(x^{5} y^{2}\) over the curve C from \((0,0)\) to \((4,2)\) is \(\frac{8192}{13}\).

Step 5 ：Final Answer: \(\boxed{\frac{8192}{13}}\)