Question

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

Answer 1

`(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)`