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By using the properties of definte, prov...

By using the properties of definte, prove that
`int_(0)^(pi//2)cos^(2)x dx=(pi)/4`

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int_(0)^(pi//4) cos^(2) x dx

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+tan^(3)x)dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3)x)/(sin^(3)x+cos^(3)x)dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(sinx)/(sinx+cosx)=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+sqrt(cotx))=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(sqrt(cotx))/(sqrt(tanx)+sqrt(cotx))=(pi)/4

By using the properties of definte, prove that int_(0)^(pi)(e^(cosx))/(e^(cosx)+e^(-cosx))dx=(pi)/2

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BETTER CHOICE PUBLICATION-INTEGRALS-ASSIGNMENT (SECTION XI MOST IMPORTANT QUESTIONS FOR PRACTICE)
  1. By using the properties of definte, prove that int(0)^(pi//2)cos^(2)...

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  2. By using the properties of definte, prove that int(0)^(pi//2)(sinx)/...

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  3. By using the properties of definte, prove that int(0)^(pi//2)(sin^(3...

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  4. By using the properties of definte, prove that int(0)^(pi//2)(sin^(3...

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  5. By using the properties of definte, prove that int(0)^(pi//2)(dx)/(1...

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  6. By using the properties of definte, prove that int(0)^(pi//2)(dx)/(1...

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  7. By using the properties of definte, prove that int(0)^(pi//2)(sqrt(c...

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  8. By using the properties of definte, prove that int(0)^(pi)(e^(cosx))...

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  9. By using the properties of definte, prove that int(0)^(a)(sqrt(x)dx)...

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  10. By using the properties of definte, prove that int(0)^(a)1/(x+sqrt(a...

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  11. Evaluate the following integrals : int(pi//6)^(pi//3)(dx)/(1+sqrt(co...

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  12. Evaluate the following integrals : int(1)^(3)(sqrt(4-x))/(sqrt(x)-sq...

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

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

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

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

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

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

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

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

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