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

Answers: 1

Show answers

Answers

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

the answer is d

the answer is in the first quadrant, which make the y-int positive.

since the dots are going down, therefore the correlation is negative

i hope it is right.

Poloma believes that the equation of the line of best fit for the following scatterplot is y=5/6x-31

Answer from: Quest

pi x^2

step-by-step explanation:

pi times x squared

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Use the frequency distribution, which shows the number of american voters (in millions) according to age, to find the probability that a voter chosen at random is in the 18 to 20 years old age range. ages frequency 18 to 20 5.9 21 to 24 7.7 25 to 34 20.4 35 to 44 25.1 45 to 64 54.4 65 and over 27.7 the probability that a voter chosen at random is in the 18 to 20 years old age range is nothing. (round to three decimal places as needed.)

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Solve the inequality and graph 6j - 7 < 5

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

choose the correct definition for extremo. a. end b. extra c. extract d. eventual

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

In the diagram, bc¯¯¯¯¯∥de¯¯¯¯¯ . what is ce ? enter your answer in the box.