216k views
4 votes
Someone help me please

Someone help me please-example-1
User Titenis
by
8.7k points

1 Answer

4 votes

9514 1404 393

Answer:

  • A = (0, 1)
  • B = (3, -2)
  • area = 4.5 square units

Explanation:

Rewriting the equations to make x the subject, we have ...

x = y² -1 . . . . . [eq1]

x = 1 - y . . . . . .[eq2]

At the points of intersection, the difference will be zero.

y² -1 -(1 -y) = 0

y² +y -2 = 0

(y -1)(y +2) = 0

The y-coordinates of points A and B are 1 and -2.

The corresponding x-coordinates are ...

x = 1 -{1, -2} = {1 -1, 1+2} = {0, 3}

Then A = (0, 1) and B = (3, -2).

__

A differential of area can be written ...

(x2 -x1)dy = ((1 -y) -(y² -1))dy = (2 -y -y²)dy

Integrating this over the interval y = [-2, 1] gives the area.


\displaystyle A=\int_(-2)^1(2-y-y^2)\,dy=\left.(2y-(1)/(2)y^2-(1)/(3)y^3)\right|_(-2)^1\\\\=\left(2-(1)/(2)-(1)/(3)\right)-\left(2(-2)-((-2)^2)/(2)-((-2)^3)/(3)\right)=(7)/(6)+4+2-(8)/(3)\\\\=\boxed{4.5}

The area of the shaded region is 4.5 square units.

Someone help me please-example-1
User Miskohut
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories