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Evaluate the following definite integrals, using calculus and showing all working: ₂∫³ 4x-4/x^2 -2x +1 dx

1 Answer

6 votes

Answer:


(16)/(3) or 5(1)/(3)

Explanation:

This question tests on the concept of integration.

Solution


\int\limits^3_2 {4x - (4)/(x^2) -2x+1} \, dx \\=\int\limits^3_2 {4x - 4x^(-2) -2x+1} \, dx \\\\

= ³₂[
4((x^(2) )/(2)) - 4((x^(-1) )/(-1) )-2((x^(2) )/(2)) +x]

=³₂[
2x^(2) + (4)/(x) -x^(2) +x]


= [2(3)^(2) +(4)/(3) -3^(2) +3] - [2(2)^2+(4)/(2) -2^(2) +2]\\=(40)/(3) -8\\=(16)/(3) or 5(1)/(3)

User Marlon Richert
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