Mathematics, 29.09.2019 00:30 wallacelizzy1

How would you use the fundamental theorem of calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240?

Answers: 1

Show answers

Answers

Answer from: maddie53116

$\displaystyle b = 11$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

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

Algebra I

Functions

Function Notation

Calculus

Integration

IntegralsDefinite IntegralsIntegration Constant C

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

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

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

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

g(x) = 4x

Interval [1, b]

A = 240

Step 2: Solve for b

Substitute in variables [Area of a Region Formula]: $\displaystyle \int\limits^b_1 {4x} \, dx = 240$ [Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle 4\int\limits^b_1 {x} \, dx = 240$ [Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle 4(\frac{x^2}{2}) \bigg| \limits^b_1 = 240$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle 4(\frac{b^2}{2} - \frac{1}{2}) = 240$ [Distributive Property] Distribute 4: $\displaystyle 2b^2 - 2 = 240$ [Addition Property of Equality] Add 2 on both sides: $\displaystyle 2b^2 = 242$ [Division Property of Equality] Divide 2 on both sides: $\displaystyle b^2 = 121$ [Equality Property] Square root both sides: $\displaystyle b = \pm 11$ Choose: $\displaystyle b = 11$

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

Unit: Integration

Book: College Calculus 10e

Answer from: Quest

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x.

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

Answer from: Quest

susie has 7 apples

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Leo has b boxes of pencils. each box contains 6 pencils. he has a total of 42 pencils. the equation that represents this situation the value of b that makes the equation true the first one is b+6=42,6b=42,b=42+6,or 42b=6 the second one are 7,836 48

Answers: 3

Answer

Mathematics, 21.06.2019 16:30

What is 96 divided by 7,488mark as brainliest

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Billy plotted −3 4 and −1 4 on a number line to determine that −3 4 is smaller than −1 4 .is he correct? explain why or why not

Answers: 3

Answer

Mathematics, 21.06.2019 22:00

Onnie is considering doing some long term investing with money that she inherited. she would like to have $50,000 at the end of 30 years. approximately how much money would lonnie need to put into an account earning 6% interest compounded annually in order to meet her goal?

Answers: 1

Answer

You know the right answer?

How would you use the fundamental theorem of calculus to determine the value(s) of b if the area und...

Questions