Mathematics, 09.01.2020 00:31 jtrill

Evaluate by using the fundamental theorem of calculus. the
integral(1 + 3y - y2)dy from 0 to 4. round to tenths.

Answers: 1

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Answer from: fansofboys

$\displaystyle \int\limits^4_0 {(1 + 3y - y^2)} \, dy = \frac{20}{3}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Calculus

Integrals

Definite Integrals

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

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

$\displaystyle \int\limits^4_0 {(1 + 3y - y^2)} \, dy$

Step 2: Integrate

[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^4_0 {(1 + 3y - y^2)} \, dy = \int\limits^4_0 {} \, dy + \int\limits^4_0 {3y} \, dy - \int\limits^4_0 {y^2} \, dy$ [2nd Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^4_0 {(1 + 3y - y^2)} \, dy = \int\limits^4_0 {} \, dy + 3\int\limits^4_0 {y} \, dy - \int\limits^4_0 {y^2} \, dy$ [Integrals] Reverse Power Rule: $\displaystyle \int\limits^4_0 {(1 + 3y - y^2)} \, dy = y \bigg| \limits^4_0 + 3(\frac{y^2}{2}) \bigg| \limits^4_0 - (\frac{y^3}{3}) \bigg| \limits^4_0$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^4_0 {(1 + 3y - y^2)} \, dy = 4 + 3(8) - \frac{64}{3}$ Simplify: $\displaystyle \int\limits^4_0 {(1 + 3y - y^2)} \, dy = \frac{20}{3}$

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

Unit: Integration

Book: College Calculus 10e

Answer from: Quest

step-by-step explanation:

ddd

Answer from: Quest

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )

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