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Integrate the function $xe^x$ from 0 to $2$

Step-by-step Solution

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Solution

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Final Answer

$8.389056$
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Step-by-step Solution

Problem to solve:

$\int_{0}^{2} xe^xdx$

Specify the solving method

1

We can solve the integral $\int xe^xdx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Unlock the first 2 steps of this solution.

Learn how to solve definite integrals problems step by step online. Integrate the function xe^x from 0 to 2. We can solve the integral \int xe^xdx 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. Solve the integral.

Final Answer

$8.389056$

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 int(xe^x)dx&0&2 using partial fractionsSolve int(xe^x)dx&0&2 using basic integralsSolve int(xe^x)dx&0&2 using u-substitutionSolve int(xe^x)dx&0&2 using integration by partsSolve int(xe^x)dx&0&2 using tabular integrationSolve int(xe^x)dx&0&2 using trigonometric substitution

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1
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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
D□x
∫
∫◻
|◻|
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:

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Main topic:

Definite Integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.05 s

Related topics:

Definite IntegralsIntegral CalculusCalculusIntegration by PartsIntegration Techniques

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