The integral of the even function f(x) from -7 to -1 is equal to -4.
How to get the integral?
Remember that an even function is a function such that:
f(-x) = f(x).
Also, remember that:
\(\int\limits^a_b {g(x)} \, dx = -\int\limits^b_a {g(x)} \, dx\)
Now we can rewrite:
\(\int\limits^{-1}_{-7} {f(x)} \, dx = -\int\limits^{-7}_{-1} {f(x)dx}\)
Because f(x) is even, we can change the negative signs:
\(\int\limits^{7}_{1} {f(x)}dx\)
This will be equal to:
\(\int\limits^{7}_{1} {f(x)}dx = \int\limits^{7}_{0} {f(x)}dx - \int\limits^{1}_{0} {f(x)}dx\)
And we know the two above ones, we will get:
\(\int\limits^{7}_{1} {f(x)}dx = 1 - 5 = -4\)
The integral is equal to -4.
If you want to learn more about integrals, you can read:
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