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

Step-by-step Solution

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Solution

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Final Answer

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

Problem to solve:

$\int_{1}^{8} x^{\frac{8}{3}}dx$

Specify the solving method

1

Simplifying

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

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

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

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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.

Final Answer

$\frac{6141}{11}$

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(x^(8/3))dx&1&8 using partial fractionsSolve int(x^(8/3))dx&1&8 using basic integralsSolve int(x^(8/3))dx&1&8 using u-substitutionSolve int(x^(8/3))dx&1&8 using integration by partsSolve int(x^(8/3))dx&1&8 using trigonometric substitution

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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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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Main topic:

Definite Integrals

Time to solve it:

~ 0.02 s

Related topics:

Definite IntegralsIntegral CalculusCalculusIntegrals of Polynomial Functions

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