How do you evaluate $int x/sqrt(1+x^2)$ from $[-sqrt2,0]$ ?

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Answer 1 · 2018-03-26T16:34:57

$1-sqrt3$

$int_-sqrt2^0x/sqrt(1+x^2)dx$

$int_-sqrt2^0x(1+x^2)^(-1/2)dx$

by inspection

$=[(1+x^2)^(1/2)]_-sqrt2^0$

$=[(1+x^2)^(1/2)]^0-[(1+x^2)^(1/2)]_-sqrt2$

$=1-(1+2)^(1/2)$

$=1-sqrt3$

How do you evaluate int x/sqrt(1+x^2)int x/sqrt(1+x^2) from [-sqrt2,0][-sqrt2,0]?