Question

I tried to figure it out but i can't. i need to show the work and i don't know how to do it.​

Answer 1

Integration Formula:

`\int\limits {x}^(n) \, dx =(x^(n+1))/(n+1) + C`

Integrate each term:

`\int\ {x^(2)} \, dx = (x^(3))/(3)`

`\int\ {x} \, dx =(x^2)/(2)`

`\int\ {5} \, dx = 5x`

`\int\ {x} \, dx =(x^2)/(2)`

`\int\ {2} \, dx = 2x`

Altogether this becomes:

`((x^3)/(3) - (x^2)/(2)-5x )/( (x^2)/(2)+2x)`

Your limits are 1 and 2. Substitute both numbers into the equation and minus them from each other.

x = 2:

`((2^3)/(3) - (2^2)/(2)-5(2) )/( (2^2)/(2)+2(2))`

-

x = 1:

`[tex]((1)/(3) - (1)/(2)-5 )/( (1)/(2)+2)`[/tex]

x = 2:

`((8)/(3) - (4)/(2)-10 )/( (4)/(2)+4)`

-

x = 1:
`((8)/(3) - 2-10 )/( 2+4)`

=

-1.212317928

Now convert all the answers to integers and see which one matches -1.212317928:

Because it's a negative number, we know it can only be A or B.

(A) = -1.212317928

(B) = -1.19047619

The answer is A:
`-(3)/(2) +In(4)/(3)`

(A) - 3/2 = ln 4/3