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Prove that : int 1/(a^(2)-x^(2)) dx = 1...

Prove that : `int 1/(a^(2)-x^(2)) dx = 1/(2a) log |(a+x)/(a-x)|+c.`

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To prove that \[ \int \frac{1}{a^2 - x^2} \, dx = \frac{1}{2a} \log \left| \frac{a+x}{a-x} \right| + C, \] we can follow these steps: ...
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GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2018-SECTION - II
  1. Let the p.m.f. of a random variable X be - P(x) = (3 -x)/10 " for ...

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  2. if int0^k (dx)/(2+8x^2)=pi/16 then find the value of k

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  3. Integrating factor of linear differential equation x(dy)/(dx) + 2y = ...

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  4. Evaluate : int e^(x) [(cos x - sin x)/(sin^(2) x)] dx.

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  5. if y = tan^(2) (log x^(3))," find " (dy)/(dx).

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  6. Find the area of ellipse x^(2)/1 + y^(2)/4 = 1.

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  7. Obtain the differential equation by eliminating the arbitrary constant...

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  8. Given X~ B (n,P) If n= 10 and p=0.4 , find E(X) and Var (X) .

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  9. Evaluate : int 1/(3+2 sin x + cos x) dx.

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  10. If x=acos^(3)t,y=asin^(3)t,"show that "(dy)/(dx)=-((y)/(x))^((1)/(3))

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  11. Examine the contionuity of the following functions at the give points ...

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  12. Find all the points of local maxima and minima and the correspondin...

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  13. Prove that : int 1/(a^(2)-x^(2)) dx = 1/(2a) log |(a+x)/(a-x)|+c.

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  14. int(-a)^(a)f(x)dx= 2int(0)^(a)f(x)dx, if f is an even function 0, if...

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  15. If f(x)(x^(2)-9)/(x-3)+alpha, "for" x gt 3 =5, "for" x =3 =2x^(2)+...

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  16. tan^(-1)((5x+1)/(3-x-6x^(2)))

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  17. A fair coin is tossed 8 times. Find the probability that it shows head...

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  18. Verify Rolle's theorem for the following function :f(x)=x^2-4x+10 on [...

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  19. Find the particular solutions of the following differential equation :...

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  20. Find the variance and standard deviation of the random variable X wh...

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