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Question Number 131810 by Fikret last updated on 08/Feb/21

$$f\left(x\right)=\{\begin{array}{l}-2x;x⩽0\\ f(x-1);x>0\end{array}$$ $$$$ $$\underset{0}{\stackrel{100}{\int }}f\left(x\right)dx=?$$

Answered by mr W last updated on 09/Feb/21

$${\int }_0^{100}f\left(x\right)dx$$ $$=\underset{k=0}{\sum ^{99}}{\int }_k^{k+1}f\left(x\right)dx$$ $$=100{\int }_{-1}^{0}f\left(x\right)dx$$ $$=100{\int }_{-1}^0(-2x)dx$$ $$=100{[-x^2]}_{-1}^0$$ $$=100$$

Commented bymr W last updated on 09/Feb/21

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