Let [ ·] represent the greatest integral function less than or equal to n tan x n sin x x. Then, find the value of lim

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A: Given that  limn→∞∑ i=1nxiln3xi+xi2Δxi0,5

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A:

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A: Given function ,     f(x)= sin x

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A: Here,

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A:

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A: Consider the function fx=2xif x≤21if x&gt;2 Here, the objective is to find the definite integral…

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A:

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A:

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A: Given:

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Q: Evaluate the definite integral.

A: The given integral i∫-π4π4x3+x4tanxdx

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A: Evaluating the integral using (a) The given integration limits: We solve it by using u-v method:…

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A:

Q: (x² – 3x}dx 170.

A:

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A: Given function :

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A: Given,

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Q: (a) '8 dx 2

A: (a)∫268 dx=[8x]26We know that ∫k dx=kx+C            = 8*6 - 8*2            = 32

Q: lim , E C [2,4| 1/2

A: The solution are next step

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Q: What is the area between the graphs of the functions f (x) = 5 sin x and g (x) = e x − 3, between x…

A: Graph of the given system is:

Q: Evaluate the definite integral by the limit definition. L (x² + 4) dx X 31

A: use the limit formula for integration

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Q: Q5. Apply the mean value theorem for integrals to evaluate e Lim -dx. 2 + CoS x

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A: limn→∞∑k=1nsinxk ∆x

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A: We have to evaluate the indefinite integral.

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Q: 3) Use long division to evaluate the indefinite integral f „s dx.

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A: NOTE: Refresh your page if you can't see any equations. .

Q: dr (x² + 1)*

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A: We need to find the following integral,

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A: Evaluate indefinite integral.

Q: Evaluate the definite integral by the limit definition

A: ∫268dxFormula:∫abcdx=cxab=cb-a   , where c is any constant.