[15 points] compute ffr2(x + 1)y2 da, r = [ 0, 1] x [0,3), by riemann sum definition. you must use the riemann sum definition to receive credit.

Looks like the integral is

where . (The inclusion of will have no effect on the value of the integral.)

Let's split up into equally-sized rectangular subintervals, and use the bottom-left vertices of each rectangle to approximate the integral. The intervals will be partitioned as

and

where the bottom-left vertices of each rectangle are given by the sequence

with and . Then the Riemann sum is

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step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)