# Answer to Question #20053 in Real Analysis for Matthew Lind

Question #20053

Consider the function on [1,5]:

f(x) =

1, x=2

-3, x=4

0, x element of [1,5], x not equal to 2, x not equal to y.

a) Show that for every epsilon greater than 0 there exist a partition P_epsilon of [1,5] such that

L(f, P_epsilon) > -epsilon, and partition Q_epsilon of [1,5] such that U(f, Q_epsilon)< epsilon.

b) Based on part a, prove that f is Reimann integrable on [1,5] and compute the integral.

f(x) =

1, x=2

-3, x=4

0, x element of [1,5], x not equal to 2, x not equal to y.

a) Show that for every epsilon greater than 0 there exist a partition P_epsilon of [1,5] such that

L(f, P_epsilon) > -epsilon, and partition Q_epsilon of [1,5] such that U(f, Q_epsilon)< epsilon.

b) Based on part a, prove that f is Reimann integrable on [1,5] and compute the integral.

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