Exercise 1 Solution

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On the interval [−1, 2], we see that g(x) > f(x).

Hint: To check that g(x) > f(x), choose a value in the interval [−1, 2], for example 0. We find that g(0) = 0 and f(0) = −4. Therefore, g(0) > f(0). What does this imply for the entire interval? Because the functions are continuous, it implies that g(x) > f(x) for the entire interval.

Another way to illustrate that g(x) is greater than f(x) over the interval [−1, 2]: Sketch the graphs of f and g on the same coordinate plane and observe that the graph of g(x) is above the graph of f(x) over the interval.

Thus,

Now, find the antiderivative and evaluate.

 

 

Hint: If your area came out negative, you have an error.