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Integrate the function $\frac{y}{y^2-y-30}$ from $9$ to $13$

Step-by-step Solution

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Final Answer

$\frac{83}{144}$
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Step-by-step Solution

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Rewrite the expression $\frac{y}{y^2-y-30}$ inside the integral in factored form

$\int_{9}^{13}\frac{y}{\left(y+5\right)\left(y-6\right)}dy$

Learn how to solve definite integrals problems step by step online.

$\int_{9}^{13}\frac{y}{\left(y+5\right)\left(y-6\right)}dy$

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Learn how to solve definite integrals problems step by step online. Integrate the function y/(y^2-y+-30) from 9 to 13. Rewrite the expression \frac{y}{y^2-y-30} inside the integral in factored form. Rewrite the fraction \frac{y}{\left(y+5\right)\left(y-6\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(y+5\right)\left(y-6\right). Multiplying polynomials.

Final Answer

$\frac{83}{144}$

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Function Plot

Plotting: $\frac{y}{y^2-y-30}$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

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