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Find : int(sin^(-1)sqrt(x)-cos^(-1)sqrt(...

Find : `int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))dx ,x in [0,1]`

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(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

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Knowledge Check

  • cos^(-1)sqrt(1-x)+sin^(-1)sqrt(1-x)=

    A
    `(pi)/(4)`
    B
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    C
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    D
    `(pi)/(2)`
    • XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
    1. Evaluate: int(x^3)/(x^4+3x^2+2)dx

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    2. Find : int(sqrt(x^2+1)(log(x^2+1)-2logx)/(x^4)dx

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    3. Find : int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)s...

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    4. In a game, a man wins rupees five for a six and loses rupee one for...

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    5. An urn contains 4 balls. Two balls are drawn at random from the urn...

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    6. Solve: tan^(-1)x+2cot^(-1)x=(2pi)/3

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    7. Find the value of cos^(-1)((x)/(2)+(sqrt(3-3x^(2)))/(2))

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    8. One kind of cake requires 200 g of flour and 25 g of fat, another k...

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    9. Using integration, find the area of the triangle PQR, coordinates o...

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    10. A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, ...

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    11. AB is a diameter of a circle and C is any point on the circumference o...

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    12. Find the distance of the point (-1,-5,-10) from the point of intersect...

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    13. Let * R*Rvec given by (a , b) vec (a+4b^2) is a binary operation. C...

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    14. The elements a(i j) of a 3xx3 matrix are given by a(i j)=1/2|-3i+j|dot...

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    15. Write the principal value of tan^(-1)[sin(-pi/2)]

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    16. If (2x4)(x-8)=0 , find the positive value of x

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    17. Write the value of |[2, 7, 65],[ 3, 8, 75],[ 5, 9, 86]|

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    18. Find int(sin^6x)/(cos^8x)dxdot

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    19. Evaluate: int(tan^(-1)x)/(1+x^2)dx

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    20. If | vec a|=8,| vec b|=3 and | vec a x vec b|=12 , find the angle betw...

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