Find the indefinite integral. (remember to use absolute values where appropriate. use c for the constant of integration.) x2 − 22x dx

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Space Space · Answer 1 · 2021-07-26T20:56:51+02:00

Answer:

[tex]\displaystyle \int {(x^2 - 22x)} \, dx = \frac{x^3}{3} - 11x^2 + C[/tex]

General Formulas and Concepts:

Calculus

Integration

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

Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {(x^2 - 22x)} \, dx[/tex]

Step 2: Integrate

[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - \int {22x} \, dx[/tex]
[2nd Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - 22\int {x} \, dx[/tex]
[Integrals] Reverse Power Rule: [tex]\displaystyle \int {(x^2 - 22x)} \, dx = \frac{x^3}{3} - 22 \Big( \frac{x^2}{2} \Big) + C[/tex]
Simplify: [tex]\displaystyle \int {(x^2 - 22x)} \, dx = \frac{x^3}{3} - 11x^2 + C[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration