Resolving an Integral by Upper and Lower Sums

[SclayP]

So, the problem statement says that i have to determinate the Upper and Lower Sums that aproximate the area under the graph given by the next function: f(x) = x^3 in the interval[0,1] with a partition of 0,2

So, i preoceeded to determinate the Upper and Lower Sums but I don't come up with the righ answer (i know because i corroborated by getting the resault of the integral \int x^3\, dx betwen 0 and 1, with my calculator)

P={0; 0,2; 0,4; 0,6; 0,8;1}
L(f,P) = \sum^{5}_{i=0}m_i(t_i-t_i-1) = (0^3)(0,2) + (0,2^3)(0,2) + (0,4^3)(0,2) + (0,6^3)(0,2) + (0,8^3)(0,2) = 0,10

That is just plain wrong but i don't know what I am doing wrong...well i won't redact how i did the Upper sums because i guess you got the point...

Thanks.

 

[SammyS]

So, the problem statement says that i have to determinate the Upper and Lower Sums that approximate the area under the graph given by the next function: f(x) = x^3 in the interval[0,1] with a partition of 0,2

So, i proceeded to determinate the Upper and Lower Sums but I don't come up with the righ answer (i know because i corroborated by getting the result of the integral \int x^3\, dx between 0 and 1, with my calculator)

P={0; 0,2; 0,4; 0,6; 0,8;1}
L(f,P) = \sum^{5}_{i=0}m_i(t_i-t_i-1) = (0^3)(0,2) + (0,2^3)(0,2) + (0,4^3)(0,2) + (0,6^3)(0,2) + (0,8^3)(0,2) = 0,10

That is just plain wrong but i don't know what I am doing wrong...well i won't redact how i did the Upper sums because i guess you got the point...

Thanks.

I get 0.016 --- or as you write it, 0,016 .

 

[SclayP]

I get 0.016 --- or as you write it, 0,016 .

Yes, sorry I posted the answer wrong, its 0.16, but what concerns me is that if i did it ok or is wrong the preocedure...

 

[SammyS]

Yes, sorry I posted the answer wrong, its 0.16, but what concerns me is that if i did it ok or is wrong the procedure...

The procedure is correct. (Lower sum)