rectangles

Question

Using n = 4 equal-width rectangles, approximate . Use the right end-point of each sub-interval to determine the height of each rectangle   Use the right end-point of each sub-interval to determine the height of each rectangle 2 (x^3 +8)dx approximate   

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                                                                                                                                           -2

 

Answer 1

I evaluated f(x) at x = -1, 0, 1 & 2, getting the following rectangle heights (at right ends):14, 16, 18, 32.

 

Since the base of each rectangle has length 1 unit, the area of the 4 rectangles is simply the sum 14+16+18+32 = 80.