Chapter 5.5, Problem 1E

To determine

To Calculate: ${\displaystyle \underset{-2}{\overset{4}{\int }}5dx}$

Answer to Problem 1E

  ${\displaystyle \underset{-2}{\overset{4}{\int }}5dx}=30$

Explanation of Solution

Given information:

  ${\displaystyle \underset{-2}{\overset{4}{\int }}5dx}$

Concept and Formula Used:

  ${\displaystyle \int x^{n}dx=\frac{x^{n+1}}{n+1}+C,}{\displaystyle \underset{a}{\overset{b}{\int }}cdx=c\left(b-a\right)}$ ,

Calculation:

It is given that

  $\begin{array}{l}{\displaystyle \underset{-2}{\overset{4}{\int }}5dx}=5{\displaystyle \underset{-2}{\overset{4}{\int }}dx}\\ \text{Using }{\displaystyle \int x^{n}dx=\frac{x^{n+1}}{n+1}+C}\\ {\displaystyle \underset{-2}{\overset{4}{\int }}5dx}=5{\left[x\right]}_{-2}^4\\ \text{Using }{\displaystyle \underset{a}{\overset{b}{\int }}cdx=c\left(b-a\right)}\\ {\displaystyle \underset{-2}{\overset{4}{\int }}5dx}=5\left[4-(-2)\right]\\ {\displaystyle \underset{-2}{\overset{4}{\int }}5dx}=30\end{array}$

Conclusion:

  ${\displaystyle \underset{-2}{\overset{4}{\int }}5dx}=30$