(a) Determine Δx and xi. Δx= xi= (b) Using the definition mentioned above, evaluate the integral. Value of integral ?
(c) evaluate the integral. Value of integral ?
(c) evaluate the integral. Value of integral ?
(a)
#Delta x = 3/n# , and#x_i=1+(3i)/n# (b)
# int_(1)^4 \ x^2+2x-5 \ dx = 21 #
By definition of an integral, then, using Riemann sums
That is
And so:
Providing for us:
By applying the meaning of f(x), we obtain:
Applying the common formula for summation:
Thus, we have:
Applying Calculus
Utilizing Calculus and our understanding of integration to determine the solution, in contrast, yields:
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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