Mathematics, 28.07.2020 21:01 krystinayagel013

The area of the region under the curve of the function f(x)=5x+7 on the interval [1,b] is 88 square units, where b>1. What is the value of b.

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Answer from: Adolfosbaby

$\displaystyle b = 5$

General Formulas and Concepts:

Calculus

Integration

Integrals

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]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

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

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^b_1 {5x + 7} \, dx = 88$

Step 2: Solve

[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^b_1 {5x} \, dx + \int\limits^b_1 {7} \, dx = 88$ [Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle 5 \int\limits^b_1 {x} \, dx + 7 \int\limits^b_1 {} \, dx = 88$ [Integrals] Integration Rule [Reverse Power Rule]: $\displaystyle 5 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^b_1 + 7(x) \bigg| \limits^b_1 = 88$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle 5 \bigg( \frac{b^2}{2} - \frac{1}{2} \bigg) + 7(b - 1) = 88$ Simplify: $\displaystyle \frac{5b^2}{2} - \frac{5}{2} + 7b - 7 = 88$ Isolate: $\displaystyle \frac{5b^2}{2} + 7b = \frac{195}{2}$ Solve: $\displaystyle b = \frac{-39}{5} ,\ 5$

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

Unit: Integration

Answer from: Quest

step-by-step explanation: you take each of the numbers and divide by the amount then you take the range

Which of the following choices is the variance of the sample shown here? 35, 36, 41, 56, 60, 71

Answer from: Quest

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

5c+2< 27 i really do not understand this.

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The area of the region under the curve of the function f(x)=5x+7 on the interval [1,b] is 88 square...

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