Question

For the following exercises, find the length of the functions over the given interval. 165, y 5x from x = 0 to x = 2

Answer 1

The length of the function y = 5x from x = 0 to x = 2 is 20.

Step-by-step explanation:

To find the length of a function over a given interval, we need to calculate the definite integral of the function over that interval. In this case, the function is y = 5x and the interval is from x = 0 to x = 2. The definite integral of y = 5x from x = 0 to x = 2 can be found by evaluating the antiderivative of the function at the upper and lower limits of the interval and subtracting the resulting values..

First, let's find the antiderivative of y = 5x, which is (5/2)x^2. We can now evaluate this antiderivative at the limits of integration:

(5/2)(2)^2 - (5/2)(0)^2 = 20 - 0 = 20.