The Riemann sum 1 * ((e^2) + (e^3) + (e^4) + (e^5)) is constructed using 4 rectangles and left endpoints. What is an integral that approximates the Riemann sum.

 

?∫26?exdx?

Step-by-step explanation

 The lefthand Riemann sum that approximates ?∫ab?f(x)dx? with N subdivisions is given by setting ?ai?:=xi?=a+iΔ? where ?Δ=Nb−a??

?L=∑i=0N−1?f(a+iΔ)Δ?

The Riemann sum 1 * ((e^2) + (e^3) + (e^4) + (e^5)) is constructed using 4 rectangles and left endpoints. What is an integral that approximates the Riemann sum.

Δ=1? , ?N=4? , ?f(x)=ex? , ?a=2?

?L=∑i=04−1?f(2+i(1))(1)?

?L=∑i=03?f(2+i(1))(1)?

?L=∑i=03?(e(2+i(1)))(1)?

?L=∑i=03?(e(2+i(1)))(1)=(e(2+(0)(1))+e(2+(1)(1))+e(2+(2)(1))+e(2+(3)(1)))(1)=(e2+e3+e4+e5)(1)?

?Δ=Nb−a??

?1=4b−2?⇒b−2=4⇒b=4+2⇒b=6?

?a=2? and ?b=6?

?∫26?exdx?

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