Try now NerdPal! Our new app on iOS and Android

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

Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

Final Answer

$\frac{5y^{3}}{5832}$
Got another answer? Verify it here!

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.

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

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

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.

Final Answer

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

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

Give us your feedback!

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
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

Used formulas:

1. See formulas

Time to solve it:

~ 0.05 s

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Including multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android app.

Join 500k+ students in problem solving.

Subscription. Cancel anytime.
Have a promo code?
Pay $2.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account
3-Month Special Plan
One-time payment of $2.97 USD.
Without automatic renewal.
Create an Account