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# Integrate the function $x^{\frac{8}{3}}$ from $1$ to $8$

## Step-by-step Solution

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###  Videos

$\frac{6141}{11}$
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##  Step-by-step Solution 

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1

Simplifying

$\int_{1}^{8}\sqrt[3]{x^{8}}dx$

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

$\int_{1}^{8}\sqrt[3]{x^{8}}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function x^(8/3) from 1 to 8. Simplifying. 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{8}{3}. Divide 1 by \frac{11}{3}. Evaluate the definite integral.

$\frac{6141}{11}$

##  Explore different ways to solve this problem

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1
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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

### Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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