The following information about the integral equation is found:
a) g(0) = 0, g(2) = 2, g(4) = 0, g(6) = - 2, g(8) = 0, g(10) = 6, g(12) = 16, g(14) = 23.
b) There is a minimum at x = 6 and a maximum at x = 14.
c) The option in the lower left corner of the third picture represents a rough graph of g(x).
How to evaluate a function equal to an integral equation
Integral equations are expressions that involves functions and integrals. In this case we find a function defined by definite integral, that is, an integral with known limits. Graphically speaking, we know that definite integral is the sum of areas "below" the curve in the given interval.
Now we evaluate the function at each point:
g(0) = 0
g(2) = 0.5 · (2) · (2) = 2
g(4) = 0.5 · (2) · (2) - 0.5 · (2) · (2) = 0
g(6) = 0.5 · (2) · (2) - 0.5 · (2) · (2) - 0.5 · (2) · (2) = -2
g(8) = 0.5 · (2) · (2) - 0.5 · (2) · (2) - 0.5 · (2) · (2) + 0.5 · (2) · (2) = 0
g(10) = 0.5 · (2) · (2) - 0.5 · (2) · (2) - 0.5 · (2) · (2) + 0.5 · (4) · (4) = 6
g(12) = 0.5 · (2) · (2) - 0.5 · (2) · (2) - 0.5 · (2) · (2) + 0.5 · (6) · (6) = 16
g(14) = 0.5 · (2) · (2) - 0.5 · (2) · (2) - 0.5 · (2) · (2) + 0.5 · (6) · (6) + 0.5 · (1) · (2) + (1) · (4) + 0.5 · (1) · (4) = 23
There is a minimum at x = 6 and a maximum at x = 14.
The option in the lower left corner of the third picture represents a rough graph of g(x).
To learn more on integral equations: https://brainly.com/question/15263893
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