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Evaluate : int(0)^((pi)/(2)) (x sin x.co...

Evaluate : `int_(0)^((pi)/(2)) (x sin x.cosx)/(sin^(4)x+cos^(4)x)dx`

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NAGEEN PRAKASHAN ENGLISH-INTEGRATION-Exercise 7p
  1. Evaluate : int(0)^(1)log ((1)/(x) -1) dx

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  2. Evaluate : int0^1x(1-x)^5dx

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  3. Evaluate : int(0)^(4) x(4-x)^(3//2)dx

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  4. Prove that :(i) int(-pi)^(pi) x^(10) sin^(7) x dx =0 (ii) int(-pi)^(...

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  5. Evaluate : int0^pi(xtan\ x)/(sec\ x+tan\ x)\ dx

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  6. Prove that :int(0)^(pi) (x)/(1 +sin^(2) x) dx =(pi^(2))/(2sqrt(2))

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  7. Prove that :int(0)^(pi) (x sin x)/(1+sinx) dx=pi((pi)/(2)-1)

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  8. Evaluate: int(-pi//2)^(pi//2)|sinx|dx

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  9. Evaluate :int(0)^(8) |x-5|dx

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  10. Evaluate :int(-pi//4)^(pi//4) |sin x|dx

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  11. "If "f(x) ={underset(x^(2)+1.2 le x le 3)(2x+1.1 le x le 2), then eva...

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  12. if f(x) ={[3x+4 , 0 le x le 2],[5x , 2 le x le 3]},then evaluate ...

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  13. Prove that :int(0)^(1) (log x)/(sqrt(1-x^(2)))dx=-(pi)/(2)log 2

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  14. Prove that :int(0)^(pi//2) x . cot x dx =(pi)/(2)log 2

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  15. Prove that :int(0)^(1)(sin^(-1)x)/(x) dx = (pi)/(2) log 2

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  16. Prove that :int(0)^(pi) (x)/(a^(2) cos^(2) x+b^(2) sin^(2) x)dx =(pi^(...

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  17. Evaluate: int0^pi(e^(cosx))/(e^(cosx)+e^(-cosx))dx

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  18. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  19. Prove that :int(0)^(oo) log (x+(1)/(x)). (dx)/(1+x^(2)) = pi log(e) 2

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  20. Evaluate : int(0)^((pi)/(2)) (x sin x.cosx)/(sin^(4)x+cos^(4)x)dx

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