Wallis' formulas. 1) Prove the formula sin"-tx cos x n-1 S sin" x dx = S sin"-2x dx 2) Use that formula to prove prove Wallis' formulas: (n-1)(n-3)...(4)(2) n(n-2)...(5)(3)(1) | (n-1)(n-3)...(5)(3)(1) n(n=2)...(4)(2) ifn >1 is odd S/ ´sin"x dx = if n > 1 is even 3) Show how the substitution u = - x shows that S2 sin" x dx = S7² cos"x dx 4) Use the formula to find 2 sin'x dx and sin®x dx

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A: use e^x expension

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A: Please go through the attached solution.  Thankyou . Best regards.

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A: Given: The integral is ∫ x29-x2 dx

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A: we have to find

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: The given functions is By solving, we get

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A: This question can be solved using the concept of integration of trigonometric functions.

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A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

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A: We know that ∫xndx=xn+1n+1Also, d(sin(x))dx=cos(x)

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A: Solution:Verify the reduction formula∫cosnx dx=cosn-1x sin xn+n-1n∫cosn-2 x dxDerive the Wallis…

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A: e-ix = cosx -i sin x If y=A sinBx then period -2πB.

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A: We will answer first 3 questions since we don't answer multiple questions at a time. Please resubmit…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.