Try now NerdPal! Our new app on iOS and Android

# Integrate the function $2\pi y^2\sqrt{y}$ from 0 to $9$

## 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

###  Videos

$3926.093219$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\int_{0}^{9}2\pi y^2\sqrt{y}dy$

Specify the solving method

1

Simplifying

$\int_{0}^{9}2\pi y^2\sqrt{y}dy$

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

$\int_{0}^{9}2\pi y^2\sqrt{y}dy$

Learn how to solve definite integrals problems step by step online. Integrate the function 2*piy^2y^1/2 from 0 to 9. Simplifying. When multiplying exponents with same base we 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 \frac{5}{2}.

$3926.093219$

##  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(2*piy^2y^1/2)dy&0&9 using partial fractionsSolve int(2*piy^2y^1/2)dy&0&9 using basic integralsSolve int(2*piy^2y^1/2)dy&0&9 using u-substitutionSolve int(2*piy^2y^1/2)dy&0&9 using integration by partsSolve int(2*piy^2y^1/2)dy&0&9 using trigonometric substitution

SnapXam A2

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

### Main topic:

Definite Integrals

~ 0.03 s

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account