Example 26 - Evaluate integral ex dx as the limit of a sum - Definate Integral as a limit of a sum

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Example 26 Evaluate ∫_0^2▒𝑒^π‘₯ 𝑑π‘₯ as the limit of a sum . Hence we can write ∫_0^2▒𝑒^π‘₯ 𝑑π‘₯ = (2βˆ’0) lim┬(nβ†’βˆž) 1/𝑛 (𝑓(0)+𝑓(0+β„Ž)+𝑓(0+2β„Ž)+……+𝑓(0+(π‘›βˆ’1)β„Ž) 𝑓(π‘₯)=𝑒^π‘₯ 𝑓(0)=𝑒^0=1 𝑓(0+β„Ž)=𝑒^(0 + β„Ž)=𝑒^β„Ž 𝑓(0+2β„Ž)=𝑒^(0 + 2β„Ž)=𝑒^2β„Ž 𝑓(0+(π‘›βˆ’1)β„Ž)=𝑒^(0 + (π‘›βˆ’1)β„Ž)=𝑒^(π‘›βˆ’1)β„Ž Thus, our equation becomes ∴ ∫_0^2▒𝑒^π‘₯ 𝑑π‘₯

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