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# Integrate the function $e^{-x^2}$ from 0 to $2$

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asin
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##  Final answer to the problem

$\frac{\sqrt{\pi }\mathrm{erf}\left(2\right)}{2}+\frac{-\sqrt{\pi }\mathrm{erf}\left(0\right)}{2}$
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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
Can't find a method? Tell us so we can add it.
1

Rewrite the function $e^{-x^2}$ as it's representation in Maclaurin series expansion

$\int\sum_{0}^{2}_{n=0}^{\infty } \frac{\left(-x^2\right)^n}{n!}dx$

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

$\int\sum_{0}^{2}_{n=0}^{\infty } \frac{\left(-x^2\right)^n}{n!}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function e^(-x^2) from 0 to 2. Rewrite the function e^{-x^2} as it's representation in Maclaurin series expansion. The power of a product is equal to the product of it's factors raised to the same power. Simplify \left(x^2\right)^n using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals n. We can rewrite the power series as the following.

##  Final answer to the problem

$\frac{\sqrt{\pi }\mathrm{erf}\left(2\right)}{2}+\frac{-\sqrt{\pi }\mathrm{erf}\left(0\right)}{2}$

$0$

##  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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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