Question - Evaluating a Definite Integral
Solution:
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.
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