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aleksandrvk [35]
2 years ago
5

Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 + 2x + 3 y2 = 2x + 12F

igure:A parabola was given in the figure

Mathematics
1 answer:
Svet_ta [14]2 years ago
3 0

Answer:

A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36

Step-by-step explanation:

The equations are:

y = x^{2} + 2x + 3

y = 2x + 12

The two graphs intersect when:

x^{2} + 2x + 3 = 2x + 12

x^{2} = 0

x_{1}  = 3\\x_{2}  = -3

To find the area under the curve for the first equation:

A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx

To find the area under the curve for the second equation:

A_{2} = \int\limits^3__-3}{2x + 12} \, dx

To find the total area:

A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx

Simplifying the equation:

A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx

Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).  

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Step-by-step explanation:

Apply PEMDAS:

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A = x

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2 years ago
Factor 5v^2 - 23v - 10​
AfilCa [17]

Answer:

(5v + 2)(v - 5)

Step-by-step explanation:

Hello!

The expression is written in the form of ax^2 + bx + c

Let's factor by grouping:

ac  = -50

The sum of the factors of -50 should add up to -23.

-25 and 2 work for this.

Expand and factor:

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The factored expression is (5v + 2)(v - 5)

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