Final answer:
To determine the area between the curve y = x^2 and the x-axis from x = 0 to x = 5, one must compute the definite integral of x^2 over that interval. The calculation results in \frac{125}{3} square units, which represents the area sought.
Step-by-step explanation:
To find the area between the curve of the function y = x^2 and the x-axis from x = 0 to x = 5, we use the concept of integration. The integral of a function represents the accumulation of the area under its graph, and in this case, we can calculate the definite integral between the two bounds.
Calculating the Area
1. Set up the integral for the function f(x) = x^2 within the interval [0, 5].
2. Perform the integration:
\[ \int_{0}^{5} x^2 dx = \left[ \frac{x^3}{3} \right]_{0}^{5} \]
3. Evaluate the integral at the bounds:
\[ = \frac{5^3}{3} - \frac{0^3}{3} = \frac{125}{3} \]
Therefore, the area between the curve y = x^2 and the x-axis from x = 0 to x = 5 is \frac{125}{3} square units.