Question

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

Answer 1

@agent0smith

Answer 2

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: \[ \int^b_a f(x)-h(x) \cdot dx \]

Answer 3

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

Answer 4

on my calculator

Answer 5

or would i just plug in points

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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.