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Evaluate sum(n=1)^(1000)int(n-1)^(n)|cos...

Evaluate `sum_(n=1)^(1000)int_(n-1)^(n)|cos2pix|dx`

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`underset(0)overset(1)int|cos2pix|dx+underset(1)overset(2)int|cos2pix|dx+"......"+underset(999)overset(1000)int|cos2pix|dx=underset(0)overset(1000)int|cos2pix|dx`
Now `|cos2pix|` is a periodic function of period `1//2`
`I = 2000 underset(0)overset(1/2)int|cos2pix|dxrArrI=2000xx2=4000`
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. Evaluate sum(n=1)^(1000)int(n-1)^(n)|cos2pix|dx

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  10. Let sequence (a(n)) be defined as a(1) = pi/4, a(n) = int(0)^(1//...

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  14. Prove that for any positive integer k , (sin2kx)/(sinx) = 2 [cosx+co...

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  15. If n gt 1. Evaluate int(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n))

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  19. Given that lim(x to oo)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1...

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