why are the integrals improper and find there convergent value1) integral from -

Question

why are the integrals improper and find there convergent value1) integral from -1 to 4 dx/root of modulus of x and 2) integral from 1 to 2 dx/x(lnx)rays to p when (p>0).

Explanation / Answer

2)? dx/xln(x) Let ln(x) = u =>dx/x = du =>? dx/xln(x) = ? du/u = ln(u) + c = ln(ln(x)) + c So applying limits 1 to 2 we get, ? dx/xln(x) = ln(ln(2)) - ln(ln(1)) = ln(ln(2)) - ln(0) = Undefined....Improper Integral. 1)? dx/sqrt(|x|) from -1 to 4 =? dx/sqrt(|x|) from -1 to 0 + ? dx/sqrt(|x|) from 0 to 4 sqrt(|x|) is not defined for -1 to 0...So improper integral.

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