Evaluating Riemann Integrals of f(x)=x^k where k>1 is an Integer

[abm]

Please Help... Riemann

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To compute the Riemann integral of f:[0,1]->R given f(x)=x^k where k>1 is an integer
1. Let m>2 and define q_m= m^(-1/m) Let P_m be the partition of [0,1] given by P_m=(0< q_m^m < q_m^(m-1)< ...< q_m <1)
Explicitly evalute L(f,P_m) and U(f,P_m)
2. Show that lim n->inf. L(f,P_m)= 1/(k+1),and lim n->inf. U(f,P_m)= 1/(k+1)
3. Show that f is integrable on [0,1]
4. Show that integra[0,1] f(x) dx= 1/(k+1)

 

[quantumdude]

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