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Question Number 20031 by mondodotto@gmail.com last updated on 20/Aug/17

Answered by Tinkutara last updated on 20/Aug/17

$$\underset{1}{\stackrel{n}{\int }}(x^2+3x)dx={[\frac{x^3}{3}+\frac{3x^2}{2}]}_1^n$$$$=\frac{n^3}{3}+\frac{3n^2}{2}-\frac{1}{3}-\frac{3}{2}=\frac{41}{6}$$$$\frac{n^3}{3}+\frac{3n^2}{2}=\frac{26}{3}$$$$2n^3+9n^2-52=0$$$$(n-2)(2n^2+13x+26)=0$$$$\Rightarrow n=2$$

Commented by mondodotto@gmail.com last updated on 20/Aug/17

$$\mathrm{thanks}$$

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