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Prove that : ""∫0 ^(pi/2)sin2xlogtanxdx=...

Prove that : `""∫_0 ^(pi/2)sin2xlogtanxdx=0`

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Using property of define integrals, prove that : int_(0)^(pi//2)sin2xlogtanx dx=0

Prove that int_0^(pi/2) sin2xlogtanxdx=0

Prove that for any positive integer k , (sin2k x)/(sinx)=2[cosx+cos3x++cos(2k-1)x]dot Hence, prove that int_0^(pi/2)sin2x kcotxdx=pi/2dot

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Using property of define integrals, prove that : int_(0)^(pi//2)logcos x dx=(-pi)/2log2

Prove that int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x)dx = 0 .

Prove that : int_(0)^(pi/4)(sqrt(tanx)+sqrt(cotx))dx=sqrt(2).pi/2 .

Evaluate : int_0^(pi/2) log sin x dx .

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=(pi)/4

MODERN PUBLICATION-MOCK TEST-2-EXERCISE
  1. Solve the following system of equations by matrix method, where xne0, ...

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  2. If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0, then pro...

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  3. If x^(y)=e^(x-y), then prove that (dy)/(dx)=(logx)/((1+logx)^(2))

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  4. If y=xlog[(ax)^-1+a^-1], prove that : x (x+1) (d^2y) / (dx^2) + xdy/dx...

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  5. Evaluate : int x^2/((x^2+1)(3x^2+4))dx

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  6. Evaluate : int1^4 (3x^2+2x)dx as the limit of sum.

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  7. Prove that : ""∫0 ^(pi/2)sin2xlogtanxdx=0

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  8. Find the particular solution of the differential equation (1+e^(2x))dy...

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  9. Using vectors, find the area of the triangle having vertices A (1, 1, ...

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  10. Find the co-ordinates of the foot of the perpendicualr drawn from the ...

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  11. There are 40 scholars in a class, out of which 10 are sports- persons....

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  12. let A = N xxN and * be the binary operation on A defined by : (a,b) * ...

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  13. Consider rrarr[4,infty] given by f(x)=x^2+4. Show that f is invertible...

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  14. Find the points of local maximum and local minimum, if any, of the fun...

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  15. Using integration find the area of region bounded by the triangle wher...

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  16. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  17. If the line (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-k)/(2)=(z)/...

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  18. Convert 5283 meters to kilometers.

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  19. An urn contains 4 white and 3 red balls. Let 'X' be the number of red ...

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  20. For three persons A, B and C the chances of being selected as Manager ...

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