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Integrate the function $\frac{y}{y^2-4y-45}$ from $12$ to $15$

Step-by-step Solution

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Solution

Final answer to the problem

$0.5036371$
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Step-by-step Solution

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Factor the trinomial $y^2-4y-45$ finding two numbers that multiply to form $-45$ and added form $-4$

$\begin{matrix}\left(5\right)\left(-9\right)=-45\\ \left(5\right)+\left(-9\right)=-4\end{matrix}$

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$\begin{matrix}\left(5\right)\left(-9\right)=-45\\ \left(5\right)+\left(-9\right)=-4\end{matrix}$

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Learn how to solve problems step by step online. Integrate the function y/(y^2-4y+-45) from 12 to 15. Factor the trinomial y^2-4y-45 finding two numbers that multiply to form -45 and added form -4. Thus. Rewrite the fraction \frac{y}{\left(y+5\right)\left(y-9\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-9\right).

Final answer to the problem

$0.5036371$

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+-4y))dy from 12 to 15 using partial fractionsSolve integral of (y/(y^2+-4y))dy from 12 to 15 using u-substitutionSolve integral of (y/(y^2+-4y))dy from 12 to 15 using integration by partsSolve integral of (y/(y^2+-4y))dy from 12 to 15 using trigonometric substitution

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Function Plot

Plotting: $\frac{y}{y^2-4y-45}$

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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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