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Please show work it’s for calc

Please show work it’s for calc-example-1
User John U
by
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2 Answers

1 vote

Answer:

-93

Explanation:

This is just.a matter of using a couple of integration rules and plugging in then using order of operations.

Difference rule and constant multiple rule will be used here.

3(-17)-7(6)

-51-42

-93

User Yucel Bayram
by
7.5k points
3 votes

Answer:


\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = -93

General Formulas and Concepts:

Calculus

Integration

  • Integrals

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

Explanation:

Step 1: Define

Identify


\displaystyle \int\limits^6_4 {f(x)} \, dx = -17


\displaystyle \int\limits^6_4 {g(x)} \, dx = 6


\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx

Step 2: Integrate

  1. [Integral] Rewrite [Integration Property - Addition/Subtraction]:
    \displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = \int\limits^6_4 {3f(x)} \, dx - \int\limits^6_4 {7g(x)} \, dx
  2. [Integrals] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = 3 \int\limits^6_4 {f(x)} \, dx - 7 \int\limits^6_4 {g(x)} \, dx
  3. [Integrals] Substitute:
    \displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = 3(-17) - 7(6)
  4. Simplify:
    \displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = -93

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

Unit: Integration

User Holdfenytolvaj
by
8.8k points

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