Question

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

Answer 1

Answer:

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

General Formulas and Concepts:

Calculus

Integration

• Integrals
• [Indefinite Integrals] Integration Constant C

Integration 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: Define

Identify

$\displaystyle \int {(x^2 - 22x)} \, dx$

Step 2: Integrate

1. [Integral] Rewrite [Integration Property - Addition/Subtraction]:               $\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - \int {22x} \, dx$
2. [2nd Integral] Rewrite [Integration Property - Multiplied Constant]:         $\displaystyle \int {(x^2 - 22x)} \, dx = \int {x^2} \, dx - 22\int {x} \, dx$
3. [Integrals] Reverse Power Rule:                                                                   $\displaystyle \int {(x^2 - 22x)} \, dx = \frac{x^3}{3} - 22 \Big( \frac{x^2}{2} \Big) + C$
4. 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