F(x)={5−1 if 1≤x< 7, if 7≤x≤13. evaluate the definite integral by interpreting it as signed area.

\int\limits^7_1 {f(x)} \, dx =24

\int\limits^13_7 {f(x)} \, dx =24

Step-by-step explanation:

From Exercise we have f(x)=5-1 , we get f(x)=4.

We calculate integral, if 1≤x<7, we get

\int\limits^7_1 {f(x)} \, dx =\int\limits^7_1 {4} \, dx =4[x]\limits^7_1=4(7-1)=4·6=24

We calculate integral, if 7≤x<13, we get

\int\limits^13_7 {f(x)} \, dx =\int\limits^13_7 {4} \, dx =4[x]\limits^13_7=

=4(13-7)=4·6=24

Therefore, we conclude that the given two integrals are the same.

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