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Integrate the function $x^{-3}$ from $- \infty $ to $-3$

Step-by-step Solution

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Final Answer

$-\frac{1}{18}$
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Step-by-step Solution

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1

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 $-3$

$\frac{x^{-2}}{-2}$

Learn how to solve differential calculus problems step by step online.

$\frac{x^{-2}}{-2}$

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Learn how to solve differential calculus problems step by step online. Integrate the function x^(-3) from -infinity to -3. 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 -3. Add the initial limits of integration. Replace the integral's limit by a finite value. Evaluate the definite integral.

Final Answer

$-\frac{1}{18}$

Exact Numeric Answer

$-0.0556$

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Function Plot

Plotting: $x^{-3}$

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Answer Assistant

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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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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