Tutorial Exercise

Evaluate the definite integral. Use a graphing utility to verify your result.

${\displaystyle \underset{0}{\overset{}{}}}(sin(x)-7)dx$

Step $1$

To evaluate the integral ${\displaystyle \underset{0}{\overset{}{}}}(sin(x)-7)dx,$ first use the property of definite integrals, that is$,$

${\displaystyle \underset{a}{\overset{b}{}}}(f(x)-g(x))dx={\displaystyle \underset{a}{\overset{b}{}}}f(x)dx-{\displaystyle \underset{a}{\overset{b}{}}}g(x)dx$

Therefore,