Evaluate the following definite integral.

10

∫ 13y / y^2-9y-22. dy

-1

33.1698

Step-by-step explanation:

10

∫ 13y / y^2-9y-22. dy

-1

Let's break down the fraction first before we integrate

13y / y^2-9y-22

= 13y / (y-11) (y+2)

=11 / (y-11) + 2 / (y+2)

Time to Integrate.

10

∫ 13y / y^2-9y-22. dy

-1

=∫ 11 / (y-11) dy + ∫ 2 / (y+2) Dy

= 11In (y-11) + 2 In (y+2)

When y = 10

= 11In (10-11) + 2In (10+2)

= 11In1 + 2In12

= 4.9698

When y = - 2

= 11In (y-11) + 2 In (y+2)

= 11In (-2-11) + 2In (-2+2)

= - 28.2

4.9698+28.2 = 33.1698