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# Compute the integral from 0 to x of f(t) for the given functions

Find a formula to compute for all for the following function .

1. .
2. The function, 3. .
4. the maximum of 1 and .

1. We know from this exercise (Section 5.5, Exercise #13) that 2. If , then over the whole integral, and so Then, if we have (Since we have so this equation works. This is the form Apostol wrote these answers as in the back of the book, so I’m getting our answers to match his. I wouldn’t have written them this way otherwise.)

Finally, if we have Since the formulas for are the same for and are the same we have for .

3. We consider two cases. If then If then 4. Since the maximum of 1 and is equal to 1 if and is equal to if we consider three cases ( , and ).

For we have For we have For we have ### One comment

1. Artem says:

I think (b) is wrong. You cannot simply convert into . The second term for the negative case (< -1) should be . The answer in Apostol is wrong, which is easy to check if you plot it.