Question

Sketch the region bounded by the graphs of f(x)=(5x)^(1/2)+2 and g(x)=x+2. Then compute the area.

Can someone explain how to solve this?

Answer 1

ok... so find the points of intersection for

\[x + 2 = (5x)^{\frac{1}{2}} + 2\]

Answer 2

would it be 5 and 0?

Answer 3

the interesting thing to note is both curves have a y-intercept of y = 2

Answer 4

yep that's good, so you get an idea about the curve

f(x) is an upper parabola with a line of symmetry y = 2

so the curve looks a bit like



hope this helps...

then the area is Area under the upper curve(f(x)) - Area under the lower curve (g(x))

hope it helps