Mathematics, 17.07.2019 13:00 tcarston1728

With calculus find the area bounded by the curve y = x^2 and the straight line y = 2 + x. a. 4 1/2 b. 4 1/6 c. 5 1/2 d. 5 1/6

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Answer from: rocksquad7917

A. 4 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Functions

Function NotationGraphing

Solving systems of equations by graphing

Calculus

Integration

IntegralsDefinite IntegralsIntegration Constant CArea under the curve

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

y = x²

y = 2 + x

Step 2: Identify

See Attachment. Find other necessary information.

Interval [-1, 2]

Step 3: Find Area

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^2_{-1} {(2 + x - x^2)} \, dx$ [Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle A = \int\limits^2_{-1} {2} \, dx + \int\limits^2_{-1} {x} \, dx - \int\limits^2_{-1} x^2} \, dx$ [1st Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle A = 2\int\limits^2_{-1} {} \, dx + \int\limits^2_{-1} {x} \, dx - \int\limits^2_{-1} x^2} \, dx$ [Integrals] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = 2(x) \bigg| \limits^2_{-1} + \frac{x^2}{2} \bigg| \limits^2_{-1} - \frac{x^3}{3} \bigg| \limits^2_{-1}$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle A = 2(3) + \frac{3}{2} - 3$ Simplify: $\displaystyle A = \frac{9}{2}$ Reduce: $\displaystyle A = 4\frac{1}{2}$

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

Unit: Integration

Book: College Calculus 10e

With calculus find the area bounded by the curve y = x^2 and the straight line y = 2 + x. a. 4 1/2

Answer from: Quest

we have three similar triangles, because each has a right angle and shares an angle. let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

$(5 + x)/6 = 6/x$

$x(x+5) = 36$

$x^2 +5x - 36 = 0$

$(x+9)(x-4) = 0$

we reject the negative root and conclude x=4

answer: 4

If bc = 6 and ad = 5, find dc. a) 4 b) 4.5 c) 7.2

Answer from: Quest

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation:

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With calculus find the area bounded by the curve y = x^2 and the straight line y = 2 + x. a. 4 1/2...