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# Integrate the function $\frac{x^3}{\sqrt{x}}$ from 0 to $4$

## Step-by-step Solution

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###  Videos

$\frac{256}{7}$
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##  Step-by-step Solution 

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Rewrite the fraction $\frac{x^3}{\sqrt{x}}$ inside the integral as the product of two functions: $x^3\frac{1}{\sqrt{x}}$

$\int_{0}^{4} x^3\frac{1}{\sqrt{x}}dx$

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

$\int_{0}^{4} x^3\frac{1}{\sqrt{x}}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function (x^3)/(x^1/2) from 0 to 4. Rewrite the fraction \frac{x^3}{\sqrt{x}} inside the integral as the product of two functions: x^3\frac{1}{\sqrt{x}}. We can solve the integral \int x^3\frac{1}{\sqrt{x}}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

$\frac{256}{7}$

##  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 integral of ((x^3)/(x^0.5))dx from 0 to 4 using partial fractionsSolve integral of ((x^3)/(x^0.5))dx from 0 to 4 using basic integralsSolve integral of ((x^3)/(x^0.5))dx from 0 to 4 using u-substitutionSolve integral of ((x^3)/(x^0.5))dx from 0 to 4 using trigonometric substitution

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Go!
1
2
3
4
5
6
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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