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# Integrate the function $\sqrt[3]{x}$ from $-1$ to $8$

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##  Final answer to the problem

$\frac{3\sqrt[3]{\left(8\right)^{4}}}{4}- \frac{3\sqrt[3]{\left(-1\right)^{4}}}{4}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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1

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 $\frac{1}{3}$

$\left[\frac{\sqrt[3]{x^{4}}}{\frac{4}{3}}\right]_{-1}^{8}$

Learn how to solve problems step by step online.

$\left[\frac{\sqrt[3]{x^{4}}}{\frac{4}{3}}\right]_{-1}^{8}$

Learn how to solve problems step by step online. Integrate the function x^(1/3) from -1 to 8. 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{1}{3}. Divide fractions \frac{\sqrt[3]{x^{4}}}{\frac{4}{3}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Evaluate the definite integral.

##  Final answer to the problem

$\frac{3\sqrt[3]{\left(8\right)^{4}}}{4}- \frac{3\sqrt[3]{\left(-1\right)^{4}}}{4}$

$12$

##  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

SnapXam A2

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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