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In: Advanced Math

6.(a) Show that if f : [a,b]→R is Riemann integrable and if m ≤ f (t)...

6.(a) Show that if f : [a,b]→R is Riemann integrable and if m ≤ f (t) ≤ M holds
for all t in the subinterval [c,d] of [a,b], then
m(d −c) ≤ ∫cd f(t) dt ≤ M(d −c). (that is supposed to be f integrated from c to d)

(b) Prove the fundamental theorem of calculus, in the form given in the Introduction
to this book. (Hint: Use part (a) to estimate F(x)−F(x0)/x−x0.)

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Expert Solution

Colby Messinger answered 4 months ago
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