(a) Find the area under the curve y = f(x) = sin x from x =...

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(a) Find the area under the curve y = f(x) = sin x from x = 0 to x = 5 by using the upper sums Un. make a partition of the interval [0, ] into n equal sub-intervals and then take If you need, you may use the following identity without Hint: the limit of Un as n→ ∞. proving it : cos(h/2) – cos((m + 1/2)h) 2 sin(h/2) sin h + sin(2h) + sin(3h) + + sin(mh) el/n + e2/n +e(n-1)/n + en/n (b) Evaluate the limit lim n00 n Hint: Use the idea of Riemann sums and definite integral. (a) Find the area under the curve y = f(x) = sin x from x = 0 to x = 5 by using the upper sums Un. make a partition of the interval [0, ] into n equal sub-intervals and then take If you need, you may use the following identity without Hint: the limit of Un as n→ ∞. proving it : cos(h/2) – cos((m + 1/2)h) 2 sin(h/2) sin h + sin(2h) + sin(3h) + + sin(mh) el/n + e2/n +e(n-1)/n + en/n (b) Evaluate the limit lim n00 n Hint: Use the idea of Riemann sums and definite integral.