Consider the integral:

Question

21
∫ x^3 dx
3
-Use all three methods to approximate this integral with n = 3
-Find the exact value of this integral

Answer 1

I have no way of knowing what "all three methods" are, I will just
do the exact value method, that is , using the regular integration method

21
∫ x^3 dx
3
= [ (1/4)x^4] from 3 to 21
= ( (1/4)(21^4) - (1/4)(3^4) )
= (1/4)(194481 - 81)
= 194400/4 = 48600

Answer 2

three methods?
Left Sum, Right Sum, Midvalue Sum, Trapezoid Rule ...
Just break it up into 3 intervals of width 6 and apply the formulas.