anonymous
  • anonymous
Evaluate the improper integral dt/( t^2-2t)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
(dt)/(t^(2)-2t) Factor out the GCF of t from each term in the polynomial. (dt)/(t(t)+t(-2)) Factor out the GCF of t from t^(2)-2t. (dt)/(t(t-2)) Reduce the expression (dt)/(t(t-2)) by removing a factor of t from the numerator and denominator. (d)/(t-2)
anonymous
  • anonymous
... separate using partial fraction then integrate easily
anonymous
  • anonymous
dt/(t^2-2t)=dt/t(t-2)=A/t +B/(t-2) now (At-2A+Bt)/t(t-2). by compairing it gives -2A=1 or A=-1/2. A+B=0 so B=1/2 now put the value of A and B. the function become....(-1/2)/t +(1/2)/(t-2) -1/2 log t +1/2 log t-2 log {squareroot of (t-2)/t} +c

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