Find the area of the region bounded by:
y=-x^2 + 5
y=-x+3

Question

Find the area of the region bounded by: 
y=-x^2 + 5
y=-x+3

anonymous · Answer

@agent0smith

anonymous · Answer

let: f(x) = -x^2 +5, h(x) = -x +3.

Find the x coordinates 'a' and 'b' of the 2 intersections by solving x for f(x) = h(x).

Then the area is given by: $$ \int^b_a f(x)-h(x) \cdot dx $$

anonymous · Answer

so how would i graph that since it's "y="

anonymous · Answer

on my calculator

anonymous · Answer

or would i just plug in points

anonymous · Answer

you graph y=f(x) and y = h(x), 2 functions on the same graph\

anonymous · Answer

idk if my calculator can graph that since it's "y="

anonymous · Answer

so how would i graph the two equations, would i plug in points for "x"?

anonymous · Answer

you can just graph:
y=-x^2 + 5
y=-x+3

anonymous · Answer

OHH okay ty can you help me with another one? :D

agent0smith · Answer

To find the points where the graphs intersect, just set them equal to each other and solve for x:

$$\large y=-x^2 + 5 $$$$\large y=-x+3$$

so let $$\large -x+3=-x^2+5$$ Now solve for x, to find your limits of integration.