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

the answer is b

Answer from: Quest

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2 polynomial long division

dividing : x4+5x3-4x2-8x+6

("dividend")

by : x-1 ("divisor")

dividend x4 + 5x3 - 4x2 - 8x + 6

- divisor * x3 x4 - x3

remainder 6x3 - 4x2 - 8x + 6

- divisor * 6x2 6x3 - 6x2

remainder 2x2 - 8x + 6

- divisor * 2x1 2x2 - 2x

remainder - 6x + 6

- divisor * -6x0 - 6x + 6

remainder 0

quotient : x3+6x2+2x-6 remainder: 0

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

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