- #1

VietDao29

Homework Helper

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I've come across some problems while reading a mathematics books.

**1.**The first problem is:

[tex]\int \max (1, x ^ 2) dx[/tex]

My answer is:

[tex]x + C, |x| \leq 1[/tex]

[tex]\frac{x ^ 3}{3} + C, |x| > 1[/tex]

But the book does not seem to agree with me. It reads:

[tex]x + C, |x| \leq 1[/tex]

[tex]\frac{x ^ 3}{3} +\frac{2}{3} \mbox{sgn} x + C, |x| > 1[/tex]

Why does the [tex]\frac{2}{3} \mbox{sgn} x[/tex] appears there?? What am I missing here?

**2.**The second problem is:

[tex]\int (|1 + x| - |1 - x|) dx[/tex]

I've never seen an absolute value in an integral before... What should I do?

Any help will be appreciated.

Viet Dao,