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int sqrt(x^2 - a^2) = 1/2 x sqrt (x^2 - ...

`int sqrt(x^2 - a^2) = 1/2 x sqrt (x^2 - a^2) - 1/2 a^2 log ( x + sqrt( x^2 - a^2) + c`

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prove that : int sqrt(x^2+a^2) dx = x/2sqrt(x^2+a^2)+a^2/2log|x+sqrt(x^2+a^2)| +c

int(1)/(sqrt(x^(2)-a^(2)))=log(x+sqrt(x^(2)-a^(2)))

int sqrt(a^(2)+x^(2))=(1)/(2)x sqrt(a^(2)+x^(2))+(1)/(2)a^(2)log(x+sqrt(a^(2)+x^(2))+c

int(1)/(sqrt(x^(2)-a^(2)))=log(x+sqrt(x^(2)-a^(2))+c

" (1) "int log(x+sqrt(x^(2)-a^(2)))dx

int_-1^1 log(x+sqrt(x^2+1))dx

int(2+sqrt(x))/((x+sqrt(x)+1)^(2))dx

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Choose the correct answer int sqrt(1+x^(2))dx is equal to (A)(x)/(2)sqrt(1+x^(2))+(1)/(2)log|(x+sqrt(x+x^(2)))|+C (B) (2)/(3)(1+x^(2))^((3)/(2))+C(C)(2)/(3)x(1+x^(2))^((3)/(2))+C(D)^(2)sqrt(1+x^(2))+(1)/(2)x^(2)log|x+sqrt(1+x^(2))|+C

GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2014-SECTION-II
  1. If y=1-costheta,x=1-sintheta,"then "(dy)/(dx)" at "theta=(pi)/(4)" is"

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  2. The integrating factor of linear differential equation (dy)/(dx) + y s...

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  3. Find the equation of the tangent to the curve y=3x^(2)-x+1 at P(1, 3).

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  4. Examine the continuity of the funciton f(x)=sinx - cos x, " for "x n...

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  5. Verify Rolle's theorem for the following function f(x) = x^2 - 5x + 9,...

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  6. intsec^nxtanxdx,n!=0

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  7. The probability mass function (p. m. f.) of X is given below : |{:(X...

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  8. Given that X ~ B( n=10, p) .If E (x) = 8, find the value of p .

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  9. If y =f(u) is differentiable function of u, and u=g(x) is a differenti...

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  10. Obtion the differential equation by elininating arbitrary constants A,...

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  11. Evaluate int(x^2+1)/((x^2+2)(2x^2+1))dx

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  12. An open box is to be made out of a piece of a square card board of sid...

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  13. Property 6: If f(x) is a continuous function defined on [0; 2a] then ...

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  14. If the function f(x) is continuous in the interval [-2, 2]. find the ...

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  15. Solve the following differential equations : (1) (dy)/(dx) = (y + s...

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  16. A fiar coin is tossed 18 times. Find the probability that it shows lea...

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  17. If x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)= ?

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  18. Find the area bounded by the cirxle x^2+y^2 =16 and the line y=x in th...

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  19. int sqrt(x^2 - a^2) = 1/2 x sqrt (x^2 - a^2) - 1/2 a^2 log ( x + sqrt(...

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  20. A random variable X has the following probability distribution : (a...

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