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Show that : int sin 7x cos 3 x dx = ...

Show that :
` int sin 7x cos 3 x dx = - [ 1/20 cos 10 x + 1/8 cos 4x ] +c `

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Show that : int cos 7 x sin 4x dx = 1/6 cos 3x - 1/22 cos 11x + c

Show that : int sqrt(1 - cos 2x ) dx = - sqrt(2) cos x + c

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Show that : int sqrt( 1+ sin 2x) dx =- sin x - cos x + c

Prove : int sin x sin 2x sin 3x dx = - 1/48 ( 6 cos 2x + 3 cos 4x - 2 cos 6 x) + c

Prove : int sin x cos 2 x cos 3 x dx = - 1/4 ((cos 2x)/2 - (cos 4x)/4 + (cos 6x)/6) + c

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CHHAYA PUBLICATION-IDENFINITE INTEGRAL -Short Answer Type Questions
  1. Evaluate the following integrals : int (cos^(3) theta - 3 cos thet...

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  2. Evaluate the following integrals : int (dx)/(sin^(2)x cos^(2) x )

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  3. Evaluate the following integrals : int (a sin^(3)x+bcos^(3)x)/(sin...

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  4. Evaluate the following integrals : int (cos^(2) x - sin^(2) x)/(sq...

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  5. Evaluate the following integrals : int tan^(-1) ((sinx)/(1- cos x...

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  6. Show that : int sqrt (1+ cos x ) dx = 2 sqrt(2) sin. x/2 + c

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  7. Show that : int sqrt(1 - cos 2x ) dx = - sqrt(2) cos x + c

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  8. Show that : int sqrt( 1+ sin 2x) dx =- sin x - cos x + c

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  9. Show that : int sqrt(1+ sin x ) dx = 2 (sin. x/2 - cos . x/2 )+ c...

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  10. Show that : int (dx)/(1+sinx)= tan x- sec x+ c

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  11. Show that : int (dx)/(1 - cosx) = - ("cosec"x + cot x) + c

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  12. Show that : int (cos x dx )/(sqrt(1+ sin x )) = 2 ( sin . x/2 + co...

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  13. Show that : int sin 7x cos 3 x dx = - [ 1/20 cos 10 x + 1/8 cos 4x...

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  14. Show that : int cos 2x cos 4x dx = (sin 6x)/12 + (sin 2x)/4 + c

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  15. Show that : int cos 7 x sin 4x dx = 1/6 cos 3x - 1/22 cos 11x + c

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  16. Show that : int sin 7 x sin 3x dx = 1/8 sin 4x - 1/20 sin 10 x ...

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  17. The slope of a curve at ( x,y) is 2x+1 . If the curve passes through ...

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  18. Find the equation of the curve whose slope at any point (x,y) is (-y) ...

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  19. Find a function whose differential is sin^(2)x cos^(2) x dx

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  20. If (dy)/(dx) = 3 sqrt(x) - 1/(sqrt(x)) , find y as a formula -of x , ...

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