Question

Area between curves, Sketch and calculate the area bounded by y=(x-2)^2, y=4-x^2, x=-1 and x=4

Answer 1

Please someone help me find a way on how to solve this.

Answer 2

do the graphs meet between -1 and 4?

Answer 3

x^2-4x+4 = 4-x^2

x^2-4x = -x^2

2x^2-4x = 0

2x(x-2) = 0 ; they appear to meet at 0 and 2

Answer 4

\[\int_{-1}^{0}f(x)-g(x)dx+\int_{0}^{2}f(x)-g(x)dx+\int_{2}^{4}f(x)-g(x)dx\]

Answer 5

personally, i just:

\[\left|\int_{-1}^{0}f(x)-g(x)dx\right|+\left|\int_{0}^{2}f(x)-g(x)dx\right|+\left|\int_{2}^{4}f(x)-g(x)dx\right|\]
in order to avoid trying to find an upper and lower function

Answer 6

thanks