Determine whether each integral is convergent or divergent E

Determine whether each integral is convergent or divergent. Evaluate those that are Convergent.

Solution

A) I= Lt _t-> [_-t⁰(1/(x+1)²+2²)+₀^t(1/(x+1)²+2²)]dx

    I=Lt _t-> [tan^-11/2-tan^-1(1-t)/2+tan^-1(1+t)/2-tan^-11/2]

    =Lt _t-> [-tan^-1(1-t)/2+tan^-1(1+t)/2]

=tan^-1()-tan^-1(-)

   =/2-(-/2)=

convergent.

B)

I=₀² (1/x(4-x²))dx

let 4-x²=p²

-2xdx=2pdp

=>

I=₂⁰ -2pdp/((p²-4)p)

=₀² dp/(p²-4)

=[1/2ln(p-2/p+2)]²₀

=ln0-ln-1

divergrent