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# Integrate the function $\frac{\frac{5}{6}\cdot 2x}{3}x$ from 0 to $\frac{y}{6}$

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##  Final answer to the problem

$\frac{5y^{3}}{5832}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

Simplifying

$\int_{0}^{\frac{y}{6}}\frac{\frac{5}{3}x}{3}xdx$

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

$\int_{0}^{\frac{y}{6}}\frac{\frac{5}{3}x}{3}xdx$

Learn how to solve definite integrals problems step by step online. Integrate the function (5/6x*2)/3x from 0 to y/6. Simplifying. Simplify the expression inside the integral. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as 2.

##  Final answer to the problem

$\frac{5y^{3}}{5832}$

##  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

SnapXam A2

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0
a
b
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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

###  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