Factor with GCF 3x^2y + 6xy

Find the area of the region enclosed by the graphs of the functions

Vaselesa [24]

Answer:

$\displaystyle A = \frac{8}{21}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Functions
Function Notation
Graphing
Solving systems of equations

Calculus

Area - Integrals

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 [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:

*Note:

Remember that for the Area of a Region, it is top function minus bottom function.

Step 1: Define

f(x) = x²

g(x) = x⁶

Bounded (Partitioned) by x-axis

Step 2: Identify Bounds of Integration

Find where the functions intersect (x-values) to determine the bounds of integration.

Simply graph the functions to see where the functions intersect (See Graph Attachment).

Interval: [-1, 1]

Lower bound: -1

Upper Bound: 1

Step 3: Find Area of Region

Integration

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx$
[Area] Rewrite [Integration Property - Subtraction]: $\displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx$
[Area] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}$
[Area] Evaluate [Integration Rule - FTC 1]: $\displaystyle A = \frac{2}{3} - \frac{2}{7}$
[Area] Subtract: $\displaystyle A = \frac{8}{21}$

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

Unit: Area Under the Curve - Area of a Region (Integration)

Book: College Calculus 10e

6 0

2 years ago

Lindsay is very excited to be getting a great deal on an iPad. It was originally $500 but she will only be paying $325. what per

Veseljchak [2.6K]

To find what she saved you need to subtract
500-325= 175
then take 175 divided by the original price (500) to get a percentage so
175÷500=0.35
0.35= 35%
so your answer is she saved 35%

6 0

2 years ago

Read 2 more answers

What does 4×(-6) equal if you solve

Naya [18.7K]

Answer:

-24

Step-by-step explanation:

Since only one of the factors has a negative sign, the product will be negative.

4 · (-6) = -24

6 0

3 years ago

Read 2 more answers

Sasha runs at a constant speed of 3.5 meters per second for hour. Then, she walks at a rate o 2 1 1.6 meters per second for hour

Nadya [2.5K]

Answer:

22

Step-by-step explanation:

4 0

2 years ago

Can someone plz help me on this plz I beg u

AfilCa [17]

Answer:

8

Step-by-step explanation:

So, lets go over a few things:

First off, all triangles have a total angle of 180 degrees.

Secondly, we know that the first two angles are 57 and 51.

Thirdly, we know that the missing angle is 9x

To solve this, we must add together the known angles, subtract them fro 180, and divide that by 9. This will give us the missing x value.

So, add together the two angles we know:

57+51

=

108

So we know 108 degrees of our triangle. We must find whats left of the 180.

To do this, subtract 108 from 180:

180-108

=

72

So our remaining angle is 72 degrres.

But recall that x isnt the misisng angle, 9x is.

So, to get x on its own, we must divide both the missing angle and 9x by 9:

72=9x

--- ---

9 9

=

8=1x

So now we know that x equals 8.

I hope this helps! :)

8 0

2 years ago

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Factor with GCF 3x^2y + 6xy - 9xy^2