Evaluate the limit using the following formula.

Question

(a) Use the definition to find an expression for the area under the curve y = x³

 from 0 to 1 as a limit. 

lim n→∞ n

i = 1

  

(0+in​)3·1n​

 

 

(b) The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit in part (a).13 + 23 + 33 +    + n3 =	n(n + 1)
2
	2

Answer 1