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

Svet_ta [14]

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).

3 0

3 years ago

jason runs 440 yards in 75 seconds.At this rate how many minutes does it take him to run a mile? (1 mile = 1,760 yards)

Zepler [3.9K]

Answer: 5 minutes

Step-by-step explanation:

We know that 1760 yards are in a mile. We can convert the given info into a proportion. 440/75 = 1760/x, where x is the number of seconds it takes to run a mile. Cross-multiply to get 440x = 75*1760. Divide both sides by 440 to get x = 75*4 = 300 seconds. The problem asks for how many minutes so you have to convert 300 seconds to minutes. To do this, we have to divide 300 by 60 to get 5 minutes.

7 0

3 years ago

What is the measure of

Irina18 [472]

The measure of angle A in the isosceles triangle ABC is equal to 120 degrees.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

In the triangle ABC, AB = BC = 8. Triangle ABC is an isosceles triangle and ∠B = ∠C = 30° (base angles are equal).

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

∠A + 30 + 30 = 180

∠A = 120°

The measure of angle A in the isosceles triangle ABC is equal to 120 degrees.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

4 0

2 years ago

Solve for p P-17=2p+3

Y_Kistochka [10]

Answer:

-20

Step-by-step explanation:

P-17=2P+3

P-2P=17+3

-P=20

Divide both sides by negative 1

P=20

7 0

3 years ago

Calculate the equation of a straight line which x-intercept is = - 2 and y-intercept = 2

VikaD [51]

Answer:

y=-2x+2

Step-by-step explanation:

it has a positive slope

the line should point like this on the graph: picture above

7 0

2 years ago