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.

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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

use formula for the circle a=3.14

step-by-step explanation:

Answer from: Quest

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !

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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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