Description
Evaluate the following integral Evaluate ( ) 4 2 1 x x dx − + 4 2 using the limit definition of the definite integral.
How exercise (due Wed5/27) Evaluate using the limit definition of the definite integral
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Explanation & Answer
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4
Evaluate ∫1 (𝑥 2 − 4𝑥 + 2)𝑑𝑥 using the limit definition of the definite integral.
4
𝑛
2
∫(𝑥 − 4𝑥 + 2)𝑑𝑥 = lim (∑ 𝑓(𝑐𝑖 )∆𝑥) , 𝑤ℎ𝑒𝑟𝑒 ∆𝑥 =
𝑛→∞
1
𝑖=1
4−1 3
=
𝑛
𝑛
∆𝑥 =
𝐻𝑒𝑟𝑒, {
𝑐𝑖 = 𝑎 + 𝑖 ∙ ∆𝑥 = 1 + 𝑖 ∙
3
𝑛
3 2
3
𝑏−𝑎
𝑛
3
𝑓(𝑐𝑖 ) = 𝑓 (1 + 𝑖 ∙ 𝑛) = (1 + 𝑖 ∙ 𝑛) − 4 (1 + 𝑖 ∙ 𝑛) + 2 = �...