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

## Step-by-step Solution

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###  Videos

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

Problem to solve:

$\int_{0}^{\frac{y}{6}}\frac{5}{6}\cdot \frac{2}{3}x\cdot xdx$

Specify the solving method

1

Simplifying

$\int_{0}^{\frac{y}{6}}\frac{5}{9}x\cdot xdx$

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

$\int_{0}^{\frac{y}{6}}\frac{5}{9}x\cdot xdx$

Learn how to solve definite integrals problems step by step online. Integrate the function 5/6x*2/3x from 0 to y/6. Simplifying. When multiplying two powers that have the same base (x), you can add the exponents. 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.

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

##  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

Solve int(5/6x*2/3x)dx&0&y/6 using partial fractionsSolve int(5/6x*2/3x)dx&0&y/6 using basic integralsSolve int(5/6x*2/3x)dx&0&y/6 using u-substitutionSolve int(5/6x*2/3x)dx&0&y/6 using integration by partsSolve int(5/6x*2/3x)dx&0&y/6 using trigonometric substitution

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5
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7
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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

### Main topic:

Definite Integrals

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