Chapter 4.3, Problem 42E

(a)

To determine

To calculate: The definite integral ${\displaystyle {\int }_0^{6}f\left(x\right)dx}$ using the values $\begin{array}{c}{\displaystyle {\int }_0^{3}f\left(x\right)dx}=4\\ {\displaystyle {\int }_3^{6}f\left(x\right)dx}=-1\end{array}$.

(b)

To determine

To calculate: The definite integral ${\displaystyle {\int }_6^{3}f\left(x\right)dx}$ using the values $\begin{array}{c}{\displaystyle {\int }_0^{3}f\left(x\right)dx}=4\\ {\displaystyle {\int }_3^{6}f\left(x\right)dx}=-1\end{array}$.

(c)

To determine

To calculate: The definite integral ${\displaystyle {\int }_3^{3}f\left(x\right)dx}$ using the values $\begin{array}{c}{\displaystyle {\int }_0^{3}f\left(x\right)dx}=4\\ {\displaystyle {\int }_3^{6}f\left(x\right)dx}=-1\end{array}$.

(d)

To determine

To calculate: The definite integral ${\displaystyle {\int }_3^6-5f\left(x\right)dx}$ using the values $\begin{array}{c}{\displaystyle {\int }_0^{3}f\left(x\right)dx}=4\\ {\displaystyle {\int }_3^{6}f\left(x\right)dx}=-1\end{array}$.