Stetson University Definite Integral Question Answer

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Stetson University

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Evaluate the following integral Evaluate ( ) 4 2 1 x x dx − + 4 2  using the limit definition of the definite integral.

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How exercise (due Wed5/27) Evaluate using the limit definition of the definite integral

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. HW exercise (due Weds 5/27) Evaluate $(x² - 4x +2)dx using the limit definition of the definite integral. 9 liji
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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 = �...


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