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Integrate the function $\left(e^x\right)^2$ from 0 to $y$

Step-by-step Solution

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Final Answer

$\frac{1}{2}e^{2y}-\frac{1}{2}$
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Step-by-step Solution

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Simplify $\left(e^x\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $x$ and $n$ equals $2$

$\int_{0}^{y} e^{2x}dx$

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

$\int_{0}^{y} e^{2x}dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function e^x^2 from 0 to y. Simplify \left(e^x\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals x and n equals 2. We can solve the integral \int_{0}^{y} e^{2x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

Final Answer

$\frac{1}{2}e^{2y}-\frac{1}{2}$

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Function Plot

Plotting: $\left(e^x\right)^2$

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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

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

2. See formulas

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