Calculate the total area of the region described. Do not count area beneath the x-axis as negative.

Bounded by the curve
y = square root of x

the x-axis, and the lines x = 0 and
x = 16

This is under Integrals, i don't know what i'm doing wrong, please help

you are integrating from y=0 to sqrtx and from the lines x=0 to 16

Area=INT (y(x)-y(0))dx from x=0 to 16

= INT sqrt(x)dx
=2/3 * x^3/2 and over the limits

= 2/3 (16^3/2-0)=2/3 (4^3) you finish

To calculate the total area of the region described, you can use the method of integration. First, let's set up the integral to find the area between the curve and the x-axis.

The given curve is y = √x. We need to find the area between this curve, the x-axis, and the lines x = 0 and x = 16.

To find the area using integration, we need to integrate the curve √x with respect to x over the interval [0, 16].

The integral setup for calculating the area is as follows:

Area = ∫[a, b] (f(x) - g(x)) dx

Where "a" and "b" represent the limits of integration (in this case, 0 and 16), f(x) represents the curve (√x), and g(x) represents the x-axis (which is y = 0).

Therefore, the integral setup for calculating the area is:

Area = ∫[0, 16] (√x - 0) dx

Simplifying further, the integral becomes:

Area = ∫[0, 16] √x dx

Now, you can solve this integral using techniques such as u-substitution or integration rules for square roots. Once you find the antiderivative, you can evaluate it from 0 to 16 to find the total area of the region.