91. Let I, = | x" cos(x³) dx and J, = | x" sin(x²)dx. (a) Find a reduction formula that expresses I, in terms of Jp–2. Hint: Write x" cos(x²) as x"-'(x cos(x²)). (b) (c) Evaluate 13. Use the result of (a) to show that I, can be evaluated explicitly if n is odd.

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A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

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A: Given,

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A: The objective of the question is checking the proper use of chain rule .

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A:

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A: We are authorised to solve only one question, please repost remaining questions. Indefinite…

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Q: (d) lim In(cos r) エ→0

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Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

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A: we use the formula ddx(ax)=ax lna

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Q: 8. 6x° cos (x³) dx

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Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

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Q: - In-2. Hence show that In = 01 tan" x dx = n - 1

A: