Use The Definition To Find An Expression For The Area Under The Curve Y = X3 From 0 To 1 As A Limit.
(a) Use Definition 2 to find an expression for the area under the curve y= (x^3) from 0 to 1 as a limit. Then use
the following formula
(1^3) + (2^3) + (3^3) +...... + (n^3) = [(n(n+1))/2]^2
to evaluate the limit.
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You should create a partition of the interval [0,1] in n subintervals that have the following lengths such that:
`Delta x_i = (1-0)/n = 1/n`
`x_i = i*(1/n)`
You need to use limit definitionto evaluate the definite integral such that:
`int_0^1 x^3 dx = lim_(n->oo) sum_(i=1)^n...
(The entire section contains 153 words.)
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