Evaluating a Definite Integral
The quality of the image isn't perfect, but I can make out that you're looking to evaluate the definite integral:
\(\int_{0}^{2} (2x) dx\)
To solve this definite integral, you can follow the steps below:
1. Find the antiderivative (indefinite integral) of the integrand function f(x) = 2x:
\[ F(x) = \int 2x dx = x^2 + C \]
where C represents the constant of integration. However, since we're evaluating a definite integral, we can ignore C.
2. Plug in the limits of integration into the antiderivative F(x):
\[ F(2) - F(0) = (2^2) - (0^2) = 4 - 0 = 4 \]
Thus, the value of the given definite integral is 4.
