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[Community Question] Calculus: Obtaining a step function given a condition

One of our user asked:

Find a step function s such that $$\int_{0}^{2} s(x) dx=5 \quad \int_{0}^{5} s(x) dx=2$$ The given answer is $$s(x)=\dfrac{5}{2} \quad \text{if} \quad 0 \leq x < 2$$

$$s(x)=-1 \quad \text{if} \quad -2 \leq x \leq 5$$

I don't understand how does one arrive to this solution.. even graphically trying to understand it I didn't come to a solution. Can someone please help me figure out how?


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[Community Question] Calculus: Asymptotic behavior of $\sum\limits_{n=0}^{\infty}x^{b^n}$

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