Integration: The Limit of a Sum

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Integration as the limit of a sum (III)

Find by the method of summation the value of:

1 4
(a) ∫ √x dx (b) ∫ 1/√x dx
0 1
1
Solution: (a) ∫ √x dx Put √x = t , then ½ 1/√x dx = dt or , dx = 2t dt
0 When x = 0 => t = 0
When x = 1 => t = 1

1
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