How do you find the area between #f(y)=y(2-y), g(y)=-y#?

Answer 1

#9/2 units^2#

Claculating the intersection Points: #x(2-x)=-x# so we get #x(3-x)=0# So we have #x_1=0# or #x_2=3# and we have #int_0^3(x(2-x)+x)dx=int_0^3(3x-x^2)dx=9/2#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

#A=int_0^3(3y-y^2)*dy=[3/2y^2-1/3y^3]_0^3=9/2#

The area between two curves due to y-axis is given by :

#color(red)[A=int_a^bx_2-x_1*dy#

#x_2=2y-y^2#

#x_1=-y#

lets find the cross between the curves:

#2y-y^2=-y rArr y^2-3y=0 rArr y(y-3)=0#

#y=3 or y=0#

#A=int_0^3(2y-y^2)-(-y)*dy#

#A=int_0^3(3y-y^2)*dy=[3/2y^2-1/3y^3]_0^3=9/2#

show the wanted area below (shaded):

#x_2=2y-y^2# red curve(green)

#x_1=-y# blue curve

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To find the area between the curves (f(y) = y(2-y)) and (g(y) = -y), you first need to determine the points of intersection. Set the equations equal to each other and solve for (y). Once you have the intersection points, integrate the absolute difference between the curves with respect to (y) over the interval of intersection. The formula for the area between two curves (f(y)) and (g(y)) from (y = a) to (y = b) is (\int_{a}^{b} |f(y) - g(y)| , dy). Apply this formula using the intersection points as limits of integration.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7