Express the integral as a limit of sums.

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SUMMARY

The integral of sin(x^4) from 0 to 6 can be expressed as a limit of sums using right endpoints. The general form of the Riemann sum is represented as Σf(xi)Δx, where xi corresponds to the right endpoints of the partition. Specifically, the limit can be expressed as Lim n → ∞ Σ sin((2i/n)^4) * (6/n), where the interval is partitioned into n subintervals. The discussion emphasizes the importance of correctly identifying the function and the partitioning method without evaluating the limit.

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  • Basic trigonometric functions and their properties
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Homework Statement



Express the integral as a limit of sums. Use right endpoints. Do not evaluate the limit.
[tex]\int[/tex]sin(x[tex]^{4}[/tex]dx from 0 to 6

Homework Equations



[tex]\sum[/tex]f(xi)[tex]\Delta[/tex]x

The Attempt at a Solution



What I'm unsure of here is what exactly the question is asking. How far do I go? Is simply saying that Lim x --> [tex]\infty[/tex][tex]\sum[/tex]sin(2i/n)[tex]^{2}[/tex] sufficient?
 
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From the fact that it mentions "use right endpoints", it is asking you for the general form of a Riemann sum of the integrand over a rectangular partition of the interval [0, 6].
 

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