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# plz plz plz help me so so important :(

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q1 /

The area of the region under the graph of f(x)=4 + 1x over the closed interval 0≤ x ≤ 1 by choosing representative point  as the right endpoint of each subinterval is given by

q2/

The approximate value of the area between the graph of f(x) = 2x2 + 1 and the interval (0,2) by choosing n = 5 rectangles is given by

Mar 11, 2021

#1
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q1 /

The area of the region under the graph of f(x)=4 + 1x over the closed interval 0≤ x ≤ 1 by choosing representative point  as the right endpoint of each subinterval is given by

You  don't specify  the width of  the sub-interval, but we  can  choose a convenient value, say, .25

The  area  in this case is the sum of [ the  rectangle widths  *  their heights ].....because  we are using the right endpoints, the area  will be over-stated

.25 (4 + .25)   +  .25 ( 4 + .50) + .25   +  .25 ( 4 + .75)  + .25 ( 4 + 1)  =

.25  [  4.25  + 4.5   + 4.75 + 5 ]    =  4.625

BTW....the TRUE  area  is  given by    ( 4 ( 1)  +  (1/2) )  =  4.5

If we  made  the  widths of  thes sub-intervals smaller, we would get  a better approximation   ....   Mar 11, 2021