Someone someone someone somone

1 answer:

8 0

Answer:

-24

Step-by-step explanation:

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Nikolay [14]

Answer:

$\displaystyle \frac{7}{24}$

General Formulas and Concepts:

<u>Algebra I</u>

<u>Calculus</u>

[Area] Limits of Riemann's Sums - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Step-by-step explanation:

<u>Step 1: Define</u>

<u /> $\displaystyle f(x) = \frac{1}{x^4} \\ \ [1, 2]$ <u />

<u />

[Integral] Set up area: $\displaystyle \int\limits^2_1 {\frac{1}{x^4}} \, dx$
[Integral] Rewrite: $\displaystyle \int\limits^2_1 {x^{-4}} \, dx$
[Integral] Reverse Power Rule: $\displaystyle \frac{-1}{3x^3} \bigg| \limits^2_1$
[Area] Fundamental Theorem of Calculus: $\displaystyle \frac{7}{24}$