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Evaluate the following integrals: (1-...

Evaluate the following integrals: (1-35) `int_(-a)^a log((a-sintheta)/(a+sintheta)) d theta ,a >0`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Evaluate:int0^(pi//2)(cosx)/(1+cosx+sinx)dx

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  2. Prove that: int0^pix/(1-cosalphasinx)dx=(pi(pi-alpha))/(sinalpha)

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  3. Evaluate the following integrals: (1-35) int(-a)^a log((a-sintheta...

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  4. Evaluate the following integrals: int(-1)^1|xcospix|dx

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  5. Evaluate the following integrals: (1-35) int0^pi(x/(1+sin^2x)+cos^7...

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  6. Evaluate : int0^pix/(1+sinalphasinx)dx

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  7. Evaluate the following integrals: (1-35) int0^(pi//2)(asinx+bcosx)/...

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  8. Evaluate the following integrals as limit of sums: int0^2(x+4)dx (...

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  9. Evaluate int1^4(x^2-\ x)\ dx as a limit of sums.

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  10. Evaluate: inta^bsinx dx using limit of sum

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  11. Mark the correct alternative in each of the following: int0^1sqrt(x...

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  12. Evaluate : int0^pi1/(1+sinx)dx

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  13. If int0^asqrt(x)dx=2aint0^(pi//2)sin^3xdx find the value of inte...

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  14. Evaluate: (i)int0^4 1/(sqrt(x^2+2x+3))dx (ii) int0^a1/(sqrt(a x-x...

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  15. If int0^1(3x^2+2x+k)dx=0, find the value of kdot

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  16. If int1^a (3x^2 + 2x +1)dx = 11 then the value of a is

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  17. If inta^b x^3dx=0, and If inta^b x^2dx=2/3, find a and b.

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  18. Evaluate: int0^(pi//2)sqrt(1-cos2x)dxdot

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  19. Evaluate: int0^(pi//2)sin^4xdx

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  20. Evaluate: int0^(pi//4)sqrt(1+sin2x)dx (ii) int0^(pi//4)sqrt(1-sin2x...

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