Mathematics, 01.03.2021 06:10 fredorivera

Please help with this question and give an explanation if possible

Answers: 3

Show answers

Answers

Answer from: eduardavezdemel

B. -15

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Calculus

Integrals

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

Integration Property [Swapping Limits]: $\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx$

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

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

Integration Property [Splitting Integral]: $\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int\limits^3_{-1} {[2g(x) + 4]} \, dx = 22$

$\displaystyle \int\limits^{-1}_{10} {g(x)} \, dx = 12$

$\displaystyle \int\limits^{10}_{3} {g(x)} \, dx = z$

Step 2: Redefine

Manipulate the given integrals.

[Integrals] Combine [Integration Property - Splitting Integral]: $\displaystyle \int\limits^{-1}_{10} {g(x)} \, dx + \int\limits^{10}_3 {g(x)} \, dx = \int\limits^3_{10} {g(x)} \, dx$ [Integrals] Rewrite: $\displaystyle \int\limits^3_{10} {g(x)} \, dx = \int\limits^{-1}_{10} {g(x)} \, dx + \int\limits^{10}_3 {g(x)} \, dx$ [Integrals] Substitute in variables: $\displaystyle \int\limits^{-1}_3 {g(x)} \, dx = 12 + z$ [Integrals] Rewrite [Integration Property - Swapping Limits]: $\displaystyle -\int\limits^3_{-1} {g(x)} \, dx = 12 + z$ [Integrals] [Division Property of equality] Isolate integral: $\displaystyle \int\limits^3_{-1} {g(x)} \, dx = -(12 + z)$ [Integrals] [Distributive Property] Distribute negative: $\displaystyle \int\limits^3_{-1} {g(x)} \, dx = -12 - z$

Step 3: Solve

[Integral] Rewrite [Integration Property - Addition]: $\displaystyle \int\limits^3_{-1} {2g(x)} \, dx + \int\limits^3_{-1} {4} \, dx = 22$ [Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle 2\int\limits^3_{-1} {g(x)} \, dx + 4\int\limits^3_{-1} \, dx = 22$ [Integral] Substitute in integral: $\displaystyle 2(-12 - z) + 4\int\limits^3_{-1} \, dx = 22$ [Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle 2(-12 - z) + 4(x) \bigg| \limits^3_{-1} = 22$ [Integral] Evaluate [Integration Rule - FTC 1]: $\displaystyle 2(-12 - z) + 4(3 - -1) = 22$ [Integral] (Parenthesis) Simplify: $\displaystyle 2(-12 - z) + 4(3 + 1) = 22$ [Integral] (Parenthesis) Add: $\displaystyle 2(-12 - z) + 4(4) = 22$ [Integral] Multiply: $\displaystyle 2(-12 - z) + 16 = 22$ [Integral] [Subtraction Property of Equality] Subtract 16 on both sides: $\displaystyle 2(-12 - z) = 6$ [Integral] [Division Property of Equality] Divide 2 on both sides: $\displaystyle -12 - z = 3$ [Integral] [Addition Property of Equality] Isolate z term: $\displaystyle -z = 15$ [Integral] [Division Property of Equality] Isolate z: $\displaystyle z = -15$ [Integral] Back-Substitute: $\displaystyle \int\limits^{10}_{3} {g(x)} \, dx = -15$

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

Unit: Integration

Book: College Calculus 10e

Answer from: Quest

16 minutes is correct

Answer from: Quest

I’m pretty sure the slope would be 1 since the x and y values increase by 1
What is the slope of the line in the graph? 3+.2+-4-2-14 1 2 3 4 5 %2+-3 +

Another question on Mathematics

Mathematics, 21.06.2019 16:30

Which choice represents the sample space ,s for this event

Answers: 3

Answer

Mathematics, 21.06.2019 18:30

David is spreading mulch on a triangular area of his flower bed. the coordinates of the vertices of the area are (1, 3), (9, 3), and (4, 6). what is the area of the triangle if each square has an area of 3 square feet?

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

What is the approximate value of q in the equation below? –1.613–1.5220.5853.079

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Find the arc length of the semicircle. 7the grade

Answers: 1

Answer

You know the right answer?

Please help with this question and give an explanation if possible
...