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1. (a) Use the graph paper provided to sketch the region bounded by the x-axis and...

1. (a) Use the graph paper provided to sketch the region bounded by the x-axis and the lines x + y = 4 and y = 3x.

(b) Shade the region you just drew above.

(c) Suppose that you were going to use Calculus to compute the area of the shaded region in part (a) above. If you chose the x-axis as your axis of integration, then how many integrals would be needed to compute this area?

(d) Suppose that you were going to use Calculus to compute the area of the shaded region in part (a) above. If you chose the y-axis as your axis of integration, then how many integrals would be needed to compute this area?

(e) Without computing it write down the integral (or integrals depending on which axis of integration you choose) that could be used to compute the area of the shaded triangle in Problem 1.a above.

(f) Compute the integral you found in part (e) above.

(g) Compute the area of the shaded region without using Calculus. Do your answers agree?

2. Find the area of the region bounded by the curves y = −x 2 + 3x and y = 2x 3 − x 2 − 5x.

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