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# Integrate the function $2\sqrt{x}$ from 0 to $2$

## Step-by-step Solution

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###  Videos

$\frac{8\sqrt{2}}{3}$
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##  Step-by-step Solution 

Problem to solve:

$\int_{0}^{2}2\sqrt{x}dx$

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1

The integral of a constant times a function is equal to the constant multiplied by the integral of the function

$2\int_{0}^{2}\sqrt{x}dx$

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

$2\int_{0}^{2}\sqrt{x}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function 2x^1/2 from 0 to 2. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. 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}{2}. Evaluate the definite integral. Simplify the expression inside the integral.

$\frac{8\sqrt{2}}{3}$

$3.771236$

##  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(2x^1/2)dx&0&2 using partial fractionsSolve int(2x^1/2)dx&0&2 using basic integralsSolve int(2x^1/2)dx&0&2 using u-substitutionSolve int(2x^1/2)dx&0&2 using integration by partsSolve int(2x^1/2)dx&0&2 using trigonometric substitution

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0
a
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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

### Main topic:

Definite Integrals

~ 0.03 s

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