Question

Find the área of the región bounded by the graphs of y=x, y=-x+4, and y=0

A) 4
B) 2
C) 8
D) no me of these

Answer 1

using the symmetry of the region
A = 2∫[0,2] (4-x)-x dx
Now just plug and chug

check: you have two triangles, each of base 4 and height 2.

Answer 2

Could you explain me more, pleaseee

Answer 3

what - the concept of an integral and areas, or just how to evaluate the integral? It's a simple application of the power rule.

Divide the area up into thin strips, each of width dx, and with height the distance between the lines.

∫ (4-x)-x dx = ∫4-2x dx = 4x - x^2
Now evaluate at the limits and subtract.

Still confused? Read your text -- I'm sure it has examples.

Answer 4

Thanks Oobleck