Final Answer
$\frac{8}{9}$
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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.
Final Answer
$\frac{8}{9}$