I have tried calc-chat's method and I always get the answer 12 units but the answer should be 69 according to my key! What do I need to do to get there??

"Use the limit process to find the area of the region between f (x)=10x+8 and the x-axis on the interval [0,3]"

To find the area of the region between a function and the x-axis using the limit process, you need to use definite integrals. Let's break down the steps to help you correctly calculate the area between f(x) = 10x + 8 and the x-axis on the interval [0,3]:

1. Start by setting up the definite integral. The formula to find the area between a function f(x) and the x-axis over an interval [a, b] is given by:

A = ∫[a, b] |f(x)| dx

In this case, the interval is [0, 3] and the function is f(x) = 10x + 8. So the integral becomes:

A = ∫[0, 3] |10x + 8| dx

2. Next, split the integral into two parts. Since |10x + 8| changes at x = -0.8 (the x-coordinate where the function changes sign), we divide the integral into two smaller integrals:

A = ∫[0, -0.8] |10x + 8| dx + ∫[-0.8, 3] |10x + 8| dx

3. Evaluate the first smaller integral. For the interval [0, -0.8], the function |10x + 8| = -(10x + 8) since it's negative in this interval. So the first integral becomes:

∫[0, -0.8] -(10x + 8) dx

Simplifying this integral will give you its value.

4. Evaluate the second smaller integral. For the interval [-0.8, 3], the function |10x + 8| = 10x + 8 since it's positive in this interval. So the second integral becomes:

∫[-0.8, 3] (10x + 8) dx

Evaluate this integral to obtain its value.

5. Add the values of both integrals to find the total area between f(x) = 10x + 8 and the x-axis on the interval [0, 3].

By going through these steps with the appropriate calculations, you should be able to obtain the correct answer.