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By using the properties of definte, prov...

By using the properties of definte, prove that
`int_(0)^(a)1/(x+sqrt(a^(2)-x^(2)))=(pi)/4`

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

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

By using the properties of definte, prove that int_(0)^(a)(sqrt(x)dx)/(sqrt(x)+sqrt(a-x))=a/2

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)(sqrt(cotx))/(sqrt(tanx)+sqrt(cotx))=(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)(e^(cosx))/(e^(cosx)+e^(-cosx))dx=(pi)/2

Using property of define integrals, prove that : int_(0)^(1) (log(1+x))/(1+x^(2))=(pi)/8log2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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