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Integrate the function $x^{\frac{1\cdot -3}{2}}$ from $1$ to $inf$

Step-by-step Solution

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Solution

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Final Answer

$-2\left(inf\right)^{-\frac{1}{2}}+2$
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Step-by-step Solution

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Simplifying

$\int_{1}^{inf} x^{-\frac{3}{2}}dx$

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$\int_{1}^{inf} x^{-\frac{3}{2}}dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function x^((1*-3)/2) from 1 to inf. Simplifying. 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{3}{2}. Divide 1 by -\frac{1}{2}. Evaluate the definite integral.

Final Answer

$-2\left(inf\right)^{-\frac{1}{2}}+2$

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 (x^(1-3/2))dx from 1 to in using partial fractionsSolve integral of (x^(1-3/2))dx from 1 to in using basic integralsSolve integral of (x^(1-3/2))dx from 1 to in using u-substitutionSolve integral of (x^(1-3/2))dx from 1 to in using integration by partsSolve integral of (x^(1-3/2))dx from 1 to in using trigonometric substitution

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Function Plot

Plotting: $x^{\frac{1\cdot -3}{2}}$

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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

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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

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