Ap calculus need help please

1 answer:

7 0

Answer:

$\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 11$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Integrals

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

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^1_0 {f(x)} \, dx = 4$

$\displaystyle \int\limits^1_0 {g(x)} \, dx = -3$

$\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx$

Step 2: Find

[Integral] Rewrite [Integration Property - Subtraction]: $\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = \int\limits^1_0 {2f(x)} \, dx - \int\limits^1_0 {g(x)} \, dx$
[1st Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 2\int\limits^1_0 {f(x)} \, dx - \int\limits^1_0 {g(x)} \, dx$
Substitute in integral values: $\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 2(4) - (-3)$
Multiply: $\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 8 - (-3)$
Subtract: $\displaystyle \int\limits^1_0 {[2f(x) - g(x)]} \, dx = 11$