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Prove that : int(0)^(1)x(1-x)^(n)dx=1/((...

Prove that : `int_(0)^(1)x(1-x)^(n)dx=1/((n+1)(n+2))`

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BETTER CHOICE PUBLICATION-INTEGRALS-ASSIGNMENT (SECTION XI MOST IMPORTANT QUESTIONS FOR PRACTICE)
  1. Evaluate the following integrals : int(1)^(3)(sqrt(4-x))/(sqrt(x)-sq...

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  2. Evaluate the following integrals : int(-8)^(8)log((2+x)/(2-x))dx

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  3. Evaluate the following integrals : int(-2)^(2)log((2+x)/(2-x))dx

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  4. Evaluate the following integrals : int0^1 |3x-1|dx

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  5. Evaluate the following integrals : int(-pi//2)^(pi//2)sin^(5)x dx

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  6. Evaluate the following integrals : int(0)^(1)|3x-1|dx

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  7. Evaluate the following integrals : int(-3)^(1)|x+2|dx

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  8. Evaluate the following integrals : int(0)^(1)|2x-1|dx

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  9. Evaluate the following integrals : intxsqrt(1+2x^2)dx

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  10. Evaluate the following integrals : int(0)^(pi)|cosx|dx

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  11. Evaluate the following integrals : int(-pi//4)^(pi//4)|sinx|dx

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  12. Prove that : int(0)^(1)x(1-x)^(n)dx=1/((n+1)(n+2))

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  13. By using the properties of definite integrals, evaluate the integral: ...

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  14. Using property of define integrals, prove that : int(0)^(pi//2)sin2x...

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  15. Using property of define integrals, prove that : int(0)^(1) (log(1+x...

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  16. Using property of define integrals, prove that : int(0)^(1) log(1/x-...

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  17. Evaluate int(2x^2-3sinx+5sqrtx)dx

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  18. Evaluate int((3-4sinx)dx)/cos^2x

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  19. Using property of define integrals, prove that : int(0)^(pi//2)logco...

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  20. Evaluate int(3xdx)/(1+2x^4)

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