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By using the properties of definite i...

By using the properties of definite integrals, evaluate the integrals `int0pi/4log(1+tanx)dx`

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A DAS GUPTA-Definite Integration-EXERCISE
  1. Evaluate the following:int0^1(x^3dx)/(1+x^4)

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  2. int0^1(x dx)/(sqrt(x+lambda)+sqrt(x+mu)),lambda!=mu

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  3. By using the properties of definite integrals, evaluate the integra...

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  4. int0^pi cos2xlogsinxdx= (A) pi (B) -pi/2 (C) pi/2 (D) none of these

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  5. Evaluate the following : int(pi//2)^(pi)e^(x)((1-sinx)/(1-cosx))dx.

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  6. integrate int0^(2pi) e^x . sin (pi/4 + x/2) dx

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  7. Evaluate the following: int0^(pi/2) |cosx-sinx|dx

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  8. Evaluate: intsqrt(2a x-x^2)dx

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

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  10. Evaluate: int2^3(2x^5+x^4-2x^3+2x^2+1)/((x^2+1)(x^4-1))dx

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  11. Evaluate the following:int0^1(x^2dx)/(1+x^3)

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  12. Evaluate: int0^(pi//2)(cos^2x)/(cos^2x+4sin^2x)dx

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  13. int(0)^((pi)/(2))(cosxdx)/(1+sin^(2)x)

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  14. Evaluate: int0^(pi/4) secx/(1+2sin^2x)dx

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  15. Evaluate the following integral:int0^(pi//2)(xsinxcosx)/(sin^4x+cos^4x...

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  16. int(pi/6)^(pi/3) (sin x+ cos x)/(sqrt(sin 2x))dx

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  17. Evaluate the following:int(-pi/4)^0sinx.sec^2(x+pi/4)dx

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  18. If f(x)=x^3,show that inta^bf(x)dx=(b-a)/6{f(a)+4f((a+b)/2)+f(b)}.

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  19. Find the value of int0^(pi/2)(sinx.cosx)/((a^2cos^2x+b^2sin^2x)^2)dx

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  20. f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,...

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