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# Integrate the function $\sqrt{x}$ from 0 to $8$

## Step-by-step Solution

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###  Videos

$12$
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##  Step-by-step Solution 

Problem to solve:

$\int_{0}^{8}\sqrt{x}dx$

Specify the solving method

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 $\frac{1}{3}$

$\left[\frac{3}{4} 1\sqrt{x^{4}}\right]_{0}^{8}$

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

$\left[\frac{3}{4} 1\sqrt{x^{4}}\right]_{0}^{8}$

Learn how to solve definite integrals problems step by step online. Integrate the function x^1/3 from 0 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 1 by \frac{4}{3}. Evaluate the definite integral. Simplify the expression inside the integral.

$12$

##  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

Solve int(x^1/3)dx&0&8 using partial fractionsSolve int(x^1/3)dx&0&8 using basic integralsSolve int(x^1/3)dx&0&8 using u-substitutionSolve int(x^1/3)dx&0&8 using integration by partsSolve int(x^1/3)dx&0&8 using trigonometric substitution

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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

~ 0.02 s

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