Hey all,

I am supposed to solve problems like these. If someone can help me with this, I should be able to figure out the rest. I just dont know which theorem to use out of all the given ones.

PS: Its the first time I'm using latex to submit a question, I was able to figure out how to adjust the image sizes, but not the spaces between words. Apologies.

$\displaystyle

Prove that \int_0^b x^3 dx = b^4/4, by

considering

partitions

into

n

equal $

$\displaystyle subintervals, using the formula \sum_{i=1}^n i^3 = n^4/4 + n^3/2 + n^2/4

$