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Evaluate: int(-1)^(3//2)|xsinpix|dx...

Evaluate: `int_(-1)^(3//2)|xsinpix|dx`

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`abs(x sin(pi x))={(xsin pix, x in (-1, 1)), (-x sin pix, x in (1, 3/2)):}`
`int_(-1)^(3//2)|xsinpix|dx=int_(-1)^(3/2)x sin pix dx+int_1^(3/2)-x sin pix dx`
`1/pi +1/pi +1/pi+ 1/(pi^2)`
`=3/pi +1/(pi^2)`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int(-pi//2)^(pi//2)|sinx|dx

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  2. Evaluate: int(-pi)^pi(cosa x+sin b x)^2dx

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  3. Evaluate: int(-1)^(3//2)|xsinpix|dx

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  4. Evaluate: int0^(2pi)cos^5x\ dx

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  5. Prove that: int0^(pi//2)logsinx\ dx=\ int0^(pi//2)logcosx\ dx=-pi/2log...

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  6. Evaluate: int0^pilog(1+cosx)dx

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  7. Evaluate the following integral: int0^(pi//2)1/(1+tanx)

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  8. Evaluate the following integral: int0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ ...

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  9. Evaluate the following integral: int0^a1/(x+sqrt(a^2-x^2))dx

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  10. Evaluate the following integral: int0^(pi//2)1/(1+cotx)dx

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  11. Evaluate the following integral: int0^(pi//2)(sin^(3//2)\ )/(sin^(3//2...

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  12. Evaluate the following integral: int0^(pi//2)1/(1+tanx)dx

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  13. Evaluate the following integral: int0^oo(logx)/(1+x^2)dx

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  14. Evaluate the following integral:int0^1("log"(1+x))/(1+x^2)dx

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  15. Evaluate the following integral:int0^pi(xtanx)/(secx\ cos e c\ x)dx

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  16. Evaluate the following integral:int0^pixsin^3x\ dx

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  17. Evaluate the following integral:int0^pi(xsinx)/(1+sinx)dx

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  18. Evaluate the following integral:int0^(pi//2)(tan^7x)/(tan^7x+cot^7x)dx

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  19. Evaluate the following integral:int0^(pi//2)x\ s in xcos^2x\ dx

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  20. Evaluate the following integral:int(-pi//2)^(pi//2)sin^3x\ dx

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