# Thread: I need help with integral calculus question!

1. ## I need help with integral calculus question!

Let S_n denote the finite sum 1 + 2^2/3 + 3^2/3 + . . . + n^2/3.

1. Calculate the integral J = ∫(b=1000;a=0) x^2/3, expressing your answer as a
positive integer.

2. Use suitable upper and lower Riemann sums for the function f(x) = x^2/3
on the interval [0, 1000] to prove that S_999 < J < S_1000.

3. Hence, or otherwise, find integer lower and upper bounds, no more than
100 units apart, for S_1000.

I sat on this for 1 hour and could not solve. Please I need a clear explanation and as simple as you can so I can understand it. Any Help appreciated

2. Originally Posted by swiftshift
Let S_n denote the finite sum 1 + 2^2/3 + 3^2/3 + . . . + n^2/3.

1. Calculate the integral J = ∫(b=1000;a=0) x^2/3, expressing your answer as a
positive integer.

2. Use suitable upper and lower Riemann sums for the function f(x) = x^2/3
on the interval [0, 1000] to prove that S_999 < J < S_1000.

3. Hence, or otherwise, find integer lower and upper bounds, no more than
100 units apart, for S_1000.

I sat on this for 1 hour and could not solve. Please I need a clear explanation and as simple as you can so I can understand it. Any Help appreciated
What have you tried so far? Can you do part 1? Do you know what a Riemann sum is? Have you got examples in class notes and textbook to follow? What progress have you made on part 2?

3. check inbox

4. Originally Posted by davidspike10
check inbox
Do not do this please. That is not what the pm system is intended for. Help is posted in the relevant thread, not sent via pm. There are good reasons for this.