The AREA bound by these two graphs is:?

Question

f(x) = x^2 - x

g(x) = -x+1

a)4/3

b)1/3

c)2/3

d)1/2

e) none of these

P.S how do u do this quick without resorting to integrals??

Answer 1

You must do this wit integral.

x^2-x = -x+1

x = 1 or x = -1

So, the bounds are -1 and 1.

Let S be the symbol of integral.

S (-x+1) - (x^2 - x) dx = S (1-x^2)dx

=x - (1/3)x^3

Put in the numbers...

(1-(1/3)) - (-1 - (-1/3)) = 4/3

So the answer is A

Answer 2

i think its b