Step-by-step Solution

Integrate $\frac{1}{x^4}$ from $3$ to $\infty $

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Step-by-step explanation

Problem to solve:

$\int_3^{\infty}\left(\frac{1}{x^4}\right)dx$

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

$\lim_{c\to\infty }\:\int_{3}^{c}\frac{1}{x^4}dx$

Unlock this full step-by-step solution!

Learn how to solve definite integrals problems step by step online. Integrate 1/(x^4) from 3 to \infty. Replace the integral's limit by a finite value. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. 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 -4. Evaluate the definite integral.

Final Answer

$\frac{1}{81}$$\,\,\left(\approx 0.012345679012345678\right)$
$\int_3^{\infty}\left(\frac{1}{x^4}\right)dx$

Main topic:

Definite integrals

Related formulas:

1. See formulas

Time to solve it:

~ 0.05 s (SnapXam)