Evaluating the definite integral ${\int}_{-4}^{4}(10{x}^{9}+7{x}^{5})dx$

s2vunov
2022-10-08
Answered

Evaluating the definite integral ${\int}_{-4}^{4}(10{x}^{9}+7{x}^{5})dx$

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Amir Hanna

Answered 2022-10-09
Author has **6** answers

Just to add to the possible solutions:

$$\begin{array}{rl}{\int}_{-4}^{4}10{x}^{9}+7{x}^{5}& ={[{x}^{10}+{\displaystyle \frac{7{x}^{6}}{6}}]}_{-4}^{4}\\ & =[{4}^{10}+{\displaystyle \frac{7\times {4}^{6}}{6}}]-[(-4{)}^{10}+{\displaystyle \frac{7(-4{)}^{6}}{6}}]\end{array}$$

$$\begin{array}{rl}& =[{4}^{10}+{\displaystyle \frac{7\times {4}^{6}}{6}}]-[(4{)}^{10}+{\displaystyle \frac{7(4{)}^{6}}{6}}]\\ & =0\end{array}$$

$$\begin{array}{rl}{\int}_{-4}^{4}10{x}^{9}+7{x}^{5}& ={[{x}^{10}+{\displaystyle \frac{7{x}^{6}}{6}}]}_{-4}^{4}\\ & =[{4}^{10}+{\displaystyle \frac{7\times {4}^{6}}{6}}]-[(-4{)}^{10}+{\displaystyle \frac{7(-4{)}^{6}}{6}}]\end{array}$$

$$\begin{array}{rl}& =[{4}^{10}+{\displaystyle \frac{7\times {4}^{6}}{6}}]-[(4{)}^{10}+{\displaystyle \frac{7(4{)}^{6}}{6}}]\\ & =0\end{array}$$

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