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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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Solution

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Final Answer

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

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Factor the trinomial $y^2-y-30$ finding two numbers that multiply to form $-30$ and added form $-1$

$\begin{matrix}\left(5\right)\left(-6\right)=-30\\ \left(5\right)+\left(-6\right)=-1\end{matrix}$

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

$\begin{matrix}\left(5\right)\left(-6\right)=-30\\ \left(5\right)+\left(-6\right)=-1\end{matrix}$

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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. Factor the trinomial y^2-y-30 finding two numbers that multiply to form -30 and added form -1. Thus. 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).

Final Answer

$\frac{83}{144}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (y/(y^2+-1y))dy from 9 to 13 using partial fractionsSolve integral of (y/(y^2+-1y))dy from 9 to 13 using basic integralsSolve integral of (y/(y^2+-1y))dy from 9 to 13 using u-substitutionSolve integral of (y/(y^2+-1y))dy from 9 to 13 using integration by parts

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Function Plot

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

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a
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n
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x
y
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.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

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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

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