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Definite integral basics challenge


It is known that the area under the curve  y=ex  from  x=0  to  x=1  is  e1; therefore we know that
01exdx=e1   and is equal to the area of the shaded region shown below.
With this knowledge, evaluate each of the following.
   (a)   10exdx=
   (b)   012exdx=
   (c)   01(2ex3)dx=