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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
- or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...
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- If y = (Sin ^-1 x)^2 + (cos^-1 x)^2, then show that (1-x^2) y 2 - xy1 ...
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- If y=x log[x// (a+bx)], show that x^3y2 - (y-xy1)^2 = 0
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- If x^3 + y^3 = 3ax^2, show that y2 + (2a^2x^2)/(y^5) = 0
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- Evaluate: int(x^2+1)/(x^4+x^2+1) dx
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- Evaluate: intdx/(sin^4x + cos^4x)
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- Evaluate: intdx((2x-x^2)^3//2)
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- Evaluate: intx^(13/2) (1+x^(5//2) )^(1/2) dx
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- Evaluate: int(log(1+x^2)dx
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- answer the foll. Questions: (ii)evaluate :int (x^4+1)/(x^6+1) dx
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- Evaluate: intdx/(sqrtsin^3x cos(x-alpha))
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- Evaluate: overset(pi)underset(0)int|cosx|dx
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- Evaluate: int (sin x + cos x)/(9 + 16 sin 2x) dx
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- Evaluate: overset(pi//4)underset(0) int(Sectheta d theta)/(1+2sin^2 ...
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- Evaluate: overset(e)underset(1)int((x+1)^3)/(x^2) dx
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- Evaluate: overset(pi)underset(0)intxsinx cos^2xdx
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- Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2.
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- Evaluate: int(pi/4)^((3pi)/4)dx/(1+cosx)
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- Evaluate : underset(nrarrinfty)lim [1/n + 1/(n+1)+ 1/(n+2) + .... +1...
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- Solve: xdy-ydx= sqrt(x^2+y^2)dx.
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