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Integrate the function $e^x-\sqrt{x}$ from 0 to $1$

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Solution

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Final Answer

$1.051615$
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Step-by-step Solution

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Expand the integral $\int_{0}^{1}\left(e^x-\sqrt{x}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int_{0}^{1} e^xdx+\int_{0}^{1}-\sqrt{x}dx$

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$\int_{0}^{1} e^xdx+\int_{0}^{1}-\sqrt{x}dx$

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Learn how to solve simplification of algebraic expressions problems step by step online. Integrate the function e^x-x^1/2 from 0 to 1. Expand the integral \int_{0}^{1}\left(e^x-\sqrt{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{1} e^xdx results in: 1.718282. The integral \int_{0}^{1}-\sqrt{x}dx results in: -\frac{2}{3}. Gather the results of all integrals.

Final Answer

$1.051615$

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 integral of (e^x+-1x^0.5)dx from 0 to 1 using partial fractionsSolve integral of (e^x+-1x^0.5)dx from 0 to 1 using basic integralsSolve integral of (e^x+-1x^0.5)dx from 0 to 1 using integration by partsSolve integral of (e^x+-1x^0.5)dx from 0 to 1 using tabular integrationSolve integral of (e^x+-1x^0.5)dx from 0 to 1 using trigonometric substitution

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Function Plot

Plotting: $e^x-\sqrt{x}$

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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

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Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.

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