why are the integrals improper and find there convergent value1) integral from -
ID: 1890359 • Letter: W
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).in the answer provided the (lnx) is raised to p. also can you answer the first qt 2nd part partdx/sqrt(|x|) from 0 to 4
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.
Explanation / Answer
improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ? or ?? or, in some cases, as both endpoints approach limits.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.