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Prove that : int0^pi (xtanx)/(secxcosecx...

Prove that : `int_0^pi (xtanx)/(secxcosecx)dx =pi^2/4`.

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BETTER CHOICE PUBLICATION-INTEGRALS-PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. Evaluate the following integrals : int(sinxdx)/sin(x-a)

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  2. Evaluate the following integrals : int(0)^(pi//2)(2logcosx-logsin 2x...

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  3. Prove that : int0^pi (xtanx)/(secxcosecx)dx =pi^2/4.

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  4. Evaluate the following as limit of sum int(1)^(3)2^(x)dx

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  5. Evaluate int((cosx-sinx)dx)/(1+sin2x)

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  6. Evaluate the following integral int((e^(5logx)-e^(4logx)) dx)/((e^(3...

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  7. Evaluate the following as limit of sum int(x+2)/(sqrt(x^(2)+2x+3))dx

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  8. Evaluate the following integrals: intx^(3)sqrt(3+5x^(4))dx

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  9. Evaluate the following integrals: int e^(x)("tan"^(-1)x+1/(1+x^(2)))...

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  10. Evaluate the following integrals: int e^(x)(log x+1/x)dx

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  11. Evaluate the following integrals: int cos^3xe^(logsinx)dx

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  12. Evaluate the following integrals: int 1/(x^(3)+1)dx

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  13. Evaluate the following integrals: int (2x+4)sqrt(x^(2)+4x+3)dx

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  14. Evaluate the following integrals: int(0)^(2)(x^(2)+3)dx

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  15. Evaluate the following integrals: int(0)^(2)(x^(3)+1)dx

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  16. Evaluate the following integrals: intcos^(4)2x dx

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  17. Evaluate the following integrals: int x(logx)^(2)dx

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  18. Evaluate the following integrals: int x cos^(-1)x dx

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  19. Evaluate the following integrals: int (dx)/(x^(2)-6x+13)

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  20. Evaluate the following integrals: int 1/(3x^(2)+13x-10)dx

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