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Integrate the function $\sqrt{x}-2\sqrt[3]{x^2}$ from 0 to $1$

Step-by-step Solution

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Final Answer

$-\frac{8}{15}$
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Step-by-step Solution

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1

Simplify the expression inside the integral

$\int_{0}^{1}\sqrt{x}dx+\int_{0}^{1}-2\sqrt[3]{x^{2}}dx$

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

$\int_{0}^{1}\sqrt{x}dx+\int_{0}^{1}-2\sqrt[3]{x^{2}}dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function x^1/2-2x^2^1/3 from 0 to 1. Simplify the expression inside the integral. The integral \int_{0}^{1}\sqrt{x}dx results in: \frac{2}{3}. The integral \int_{0}^{1}-2\sqrt[3]{x^{2}}dx results in: -\frac{6}{5}. Gather the results of all integrals.

Final Answer

$-\frac{8}{15}$

Exact Numeric Answer

$-0.5333$

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Function Plot

Plotting: $\sqrt{x}-2\sqrt[3]{x^2}$

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1
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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
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

How to improve your answer:

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

Used Formulas

1. See formulas

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