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# Integrate the function $\frac{2}{t^3}$ from $1$ to $3$

## Step-by-step Solution

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###  Videos

$\frac{8}{9}$
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##  Step-by-step Solution 

Problem to solve:

$\int_{1}^{3}\frac{2}{t^3}dt$

Specify the solving method

1

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int_{1}^{3}2t^{-3}dt$

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

$\int_{1}^{3}2t^{-3}dt$

Learn how to solve definite integrals problems step by step online. Integrate the function 2/(t^3) from 1 to 3. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. 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. Evaluate the definite integral.

$\frac{8}{9}$

$0.8889$

##  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(2/(t^3))dt&1&3 using partial fractionsSolve int(2/(t^3))dt&1&3 using basic integralsSolve int(2/(t^3))dt&1&3 using u-substitutionSolve int(2/(t^3))dt&1&3 using integration by partsSolve int(2/(t^3))dt&1&3 using trigonometric substitution

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5
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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

### Main topic:

Definite Integrals

~ 0.04 s

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