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

Step-by-step Solution

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e
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ln
log
log
lim
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θ
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<
>=
<=
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

$3926.093219$
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

When multiplying exponents with same base we can add the exponents

$\int_{0}^{9}2\pi \sqrt{y^{5}}dy$

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

$\int_{0}^{9}2\pi \sqrt{y^{5}}dy$

Unlock the first 2 steps of this solution!

Learn how to solve definite integrals problems step by step online. Integrate the function 6.283185307179586y^2y^1/2 from 0 to 9. 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}. Evaluate the definite integral.

Final Answer

$3926.093219$
SnapXam A2
Answer Assistant

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Got another 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

Useful tips on how to improve your answer:

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

Main topic:

Definite Integrals

Time to solve it:

~ 0.04 s