Find the arc length of the curve y = 2x^3/2 from x = 0 to x = 5. Approximate area to two decimal places. A) 23.04 $\pi$ B) 310.99 C) 310.99 $\pi$ D) 23.11 E) 23.04

Question

Quizplus · Accepted Answer

The given curve is $y = 2x^{3/2}$. To find the arc length from $x = 0$ to $x = 5$, we use the formula for arc length in terms of $x$, which is $L = \int_{a}^{b} \sqrt{1 + (\frac{dy}{dx})^2} dx$. First, we find the derivative of $y$ with respect to $x$, which is $\frac{dy}{dx} = 3x^{1/2}$. Plugging this into the formula gives us an integral that, when evaluated from $x = 0$ to $x = 5$, yields an approximate value of 23.04. This calculation involves integrating the square root of $1 + (3x^{1/2})^2$, simplifying, and then evaluating the definite integral.

Find the Arc Length of the Curve Y = 2x3/2 π\piπ

Find the Arc Length of the Curve Y = 2x^3/2 $\pi$