# Introduction to Integrals

### Problems for "The Area as a Sum"

Problem : Consider the function f (x) = x 2 + 1 on the interval [0, 2] . Using four subdivisions, find the left-hand approximation, L 4 , of the area under the curve of f on the interval indicated.

Problem : For the same function, using four subdivisions, find the right-hand sum, R 4 .

Problem : For the same function, using four subdivisions, find the midpoint sum, M 4 .

Problem : Find

 f (x k)Δx for f (x) = 2x on [0, 2]

Problem : Find

 f (x k)Δx for f (x) = on [0, 3]

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