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Prove that int0^(pi/2)lnSinxdx=-pi/2ln2...

Prove that `int_0^(pi/2)lnSinxdx=-pi/2ln2`

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SHARAM PUBLICATION-MODEL QUESTION PAPER -17-EXERCISE
  1. Evaluate int(x+sqrt(x^2+a^2))dx

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  2. Evaluate intcosec^2xsqrt(cotx)dx

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  3. Prove that int0^(pi/2)lnSinxdx=-pi/2ln2

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  4. Determine the area of the region between the curves y=cosx and y=sinx,...

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  5. Find the general solution of the differential equation (1+x^2) tan^-1y...

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  6. Prove that f:RrightarrowR such that f(x)=frac[2x^2][x^2+1] is neither ...

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  7. Let A={1, 2, 3, 5}, B={4, 6, 9}, A relation R form A to B is defined b...

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  8. Consider the binary operation ** on the set {1, 2, 3, 4 5} defined by ...

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  9. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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  10. Find the maixmum value of z =50x1+60x2 subject to 2x1+3x2le6,x1,x2ge0

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  11. Write the values of a and b, for which the vectors (a-1)hat(i) + (b+2)...

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  12. Find the scalar projection of the vector veca = 3hati+6hatj + 9hatk on...

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  13. Find the co-ordinates of the point where the perpendicular from the or...

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  14. Find the equation of the plane passing through the line x = y = z and ...

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  15. Find the co-ordinates of the point where the line (x-2)/3=(y+1)/4=(z-2...

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  16. Find (dy)/(dx) when x^y+y^x=a^b

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  17. Evaluate inte^x((1+sinx)/(1+cosx))dx.

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  18. intsin^-1sqrt(x/(a+x))dx=.

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  19. Find the area of the region in the first quadrant bounded by x - axis,...

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  20. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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