Chapter 4.3, Problem 43E

(a)

To determine

To calculate: The definite integral ${\displaystyle {\int }_2^6\left(f\left(x\right)+g\left(x\right)\right)dx}$ using the provided values ${\displaystyle {\int }_2^{6}f\left(x\right)dx}=10$ and ${\displaystyle {\int }_2^{6}g\left(x\right)dx}=-2$

(b)

To determine

To calculate: The definite integral ${\displaystyle {\int }_2^6\left(g\left(x\right)-f\left(x\right)\right)dx}$ using the provided values ${\displaystyle {\int }_2^{6}f\left(x\right)dx}=10$ and ${\displaystyle {\int }_2^{6}g\left(x\right)dx}=-2$

(c)

To determine

To calculate: The definite integral ${\displaystyle {\int }_2^{6}2g\left(x\right)dx}$ using the provided values ${\displaystyle {\int }_2^{6}f\left(x\right)dx}=10$ and ${\displaystyle {\int }_2^{6}g\left(x\right)dx}=-2$

(d)

To determine

To calculate: The definite integral ${\displaystyle {\int }_2^{6}3f\left(x\right)dx}$ using the provided values ${\displaystyle {\int }_2^{6}f\left(x\right)dx}=10$ and ${\displaystyle {\int }_2^{6}g\left(x\right)dx}=-2$