How do you find the area of the region between the graphs of #y=x^2# and #y=-x# from x=0 to x=3?

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Answer 1 · 2017-03-25T16:19:41

Given two functions, f(x) and g(x), where f(x) > g(x) in a region [a,b] the area between the two functions is:

#A = int_a^b(f(x)-g(x))dx#

In the region [0,3], f(x) = x^2 and g(x) =-x.

Therefore the area of the between the two function in this region is:

#A = int_0^3(x^2+x)dx#

#A =x^3/3+x^2/2|_0^3#

#A = (3^3/3+3^2/2) - (0^3/3+0^2/2)#

#A = 27/2#