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Find the integral $\pi ^2\int_{0}^{2} x^3\left(3-x\right)dx$

Step-by-step Solution

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sin
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asin
acos
atan
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$55.269785$
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Step-by-step Solution

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1

Calculate the power $\pi ^2$

$\pi^{2}\int_{0}^{2} x^3\left(3-x\right)dx$

Learn how to solve integral calculus problems step by step online.

$\pi^{2}\int_{0}^{2} x^3\left(3-x\right)dx$

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Learn how to solve integral calculus problems step by step online. Find the integral int(x^3(3-x))dx&0&2pi^2. Calculate the power \pi ^2. Rewrite the integrand x^3\left(3-x\right) in expanded form. Expand the integral \int_{0}^{2}\left(3x^3-x^{4}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the product \pi^{2}\left(\int_{0}^{2}3x^3dx+\int_{0}^{2}-x^{4}dx\right).

Final Answer

$55.269785$

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5
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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

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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