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How do you calculate the area enclosed between curves?

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Please see the attached file for the three problems.

Question 16:
Give the are of the region bounded by the graphs of
R(x) = -x^2 + 6
G(x) = x
and the vertical line x = 3.

Question 17:
Give the area of the region bounded by the graphs of
R(x) = -x^2 + 3
G(x) = -2x
and the vertical line x = -2.

Question 18:
Give the area of the region bounded by the graphs of
R(x) = -x^2 + 5
G(x) = -4x
and the vertical lines x = -2 and x = 6.

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Solution Summary

The solutions to three problems on areas enclosed between curves are provided in an attached Word document.

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Question 16
Give the area of the region bounded by the graphs of

and the vertical line x = 3.
a)
b)
c)
d)
e)
f) None of the above.

The two curves intersect at x = -3 and x = 2

Total area =  (6 - x^2 - x)dx over [-3, 2] +  (x + x^2 - 6) dx over [2, 3]
= (6x ...

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