Problems And Solutions Pdf - Riemann Integral

# Riemann Integral: Problems and Solutions Problem 1 Compute the Riemann sum for f(x) = x² on [0,2] using 4 subintervals and right endpoints.

0 ≤ sin x ≤ 1 and 1 ≤ 1+x² ≤ 1+(π/2)², but simpler: 0 ≤ f(x) ≤ 1 ⇒ 0 ≤ I ≤ π/2. Lower bound π/6 comes from sin x ≥ 2x/π? Accept as given. riemann integral problems and solutions pdf

\subsection*Solution 3 No. For any partition, upper sum (U(P,f)=1) (since every interval contains rationals), lower sum (L(P,f)=0) (since every interval contains irrationals). Thus (\inf U \neq \sup L), so (f) is not Riemann integrable. # Riemann Integral: Problems and Solutions Problem 1