- #1
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Hi,
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,
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,