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:

$\int\limits {x}^{n} \, dx =\frac{x^{n+1}}{n+1} + C$

Integrate each term:

$\int\ {x^{2}} \, dx = \frac{x^{3}}{3}$

$\int\ {x} \, dx =\frac{x^2}{2}$

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

$\int\ {x} \, dx =\frac{x^2}{2}$

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

Altogether this becomes:

$\frac{\frac{x^3}{3} - \frac{x^2}{2}-5x }{ \frac{x^2}{2}+2x}$

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

x = 2:

$\frac{\frac{2^3}{3} - \frac{2^2}{2}-5(2) }{ \frac{2^2}{2}+2(2)}$

-

x = 1:

$[tex]\frac{\frac{1}{3} - \frac{1}{2}-5 }{ \frac{1}{2}+2}$[/tex]

x = 2:

$\frac{\frac{8}{3} - \frac{4}{2}-10 }{ \frac{4}{2}+4}$

-

x = 1: $\frac{\frac{8}{3} - 2-10 }{ 2+4}$

=

-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: $-\frac{3}{2} +In\frac{4}{3}$

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