Question

Evaluate the following definite integral. 10 ∫ 13y/ y^2-9y-22 .dy -1

Answer 1

Answer:

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