Q:

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

Accepted Solution

A:
Answer:$$\displaystyle \int {(x^2 - 22x)} \, dx = \frac{x^3}{3} - 11x^2 + C$$General Formulas and Concepts:CalculusIntegrationIntegrals[Indefinite Integrals] Integration Constant CIntegration Rule [Reverse Power Rule]:                                                               $$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$$Integration Property [Multiplied Constant]:                                                         $$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$$Integration Property [Addition/Subtraction]:                                                       $$\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$$Step-by-step explanation:Step 1: DefineIdentify$$\displaystyle \int {(x^2 - 22x)} \, dx$$Step 2: Integrate[Integral] Rewrite [Integration Property - Addition/Subtraction]:               $$\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - \int {22x} \, dx$$[2nd Integral] Rewrite [Integration Property - Multiplied Constant]:         $$\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - 22\int {x} \, dx$$[Integrals] Reverse Power Rule:                                                                   $$\displaystyle \int {(x^2 - 22x)} \, dx = \frac{x^3}{3} - 22 \Big( \frac{x^2}{2} \Big) + C$$Simplify:                                                                                                         $$\displaystyle \int {(x^2 - 22x)} \, dx = \frac{x^3}{3} - 11x^2 + C$$Topic: AP Calculus AB/BC (Calculus I/I + II)Unit:  Integration