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# Integrate the function $\sqrt[5]{x^{2}}$ from 0 to $2$

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##  Final answer to the problem

$\frac{5\sqrt[5]{\left(2\right)^{7}}}{7}- \frac{5\sqrt[5]{\left(0\right)^{7}}}{7}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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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 $\frac{2}{5}$

$\left[\frac{\sqrt[5]{x^{7}}}{\frac{7}{5}}\right]_{0}^{2}$

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

$\left[\frac{\sqrt[5]{x^{7}}}{\frac{7}{5}}\right]_{0}^{2}$

Learn how to solve definite integrals problems step by step online. Integrate the function x^(2/5) from 0 to 2. 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{2}{5}. Divide fractions \frac{\sqrt[5]{x^{7}}}{\frac{7}{5}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Evaluate the definite integral.

##  Final answer to the problem

$\frac{5\sqrt[5]{\left(2\right)^{7}}}{7}- \frac{5\sqrt[5]{\left(0\right)^{7}}}{7}$

$1.885011$

##  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

SnapXam A2

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a
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v
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x
y
z
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(◻)
+
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×
◻/◻
/
÷
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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