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If l=int(sqrt(tanx)+sqrt(cotx))dx=f(x)+c...

If `l=int(sqrt(tanx)+sqrt(cotx))dx=f(x)+c` then `f(x)` is equal to

A

`sqrt(2)sin^(-1)(sinx-cosx)`

B

`(pi)/(sqrt(2))-sqrt(2)cos^(-1)(sinx-cosx)`

C

`sqrt(2)tan^(-1)((tanx-1)/(sqrt(2tanx)))`

D

`sin2x`

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AAKASH INSTITUTE-INTEGRALS-Objective Type Questions (More than one answer)
  1. int(dx)/(sqrt(x^(2)+2x+1))=Alog|x+1|+C, x ne 1 then

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  2. The value of int(x^(2)+cos^(2)x)/(1+x^(2))"cosec"^(2)x dx is equal to:

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  3. If l=int(sqrt(tanx)+sqrt(cotx))dx=f(x)+c then f(x) is equal to

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  4. int(dx)/(5+4cosx)=lambdatan^(-1)(mtan.(x)/(2))+C then

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  5. inte^(sin^(2)x)(cosx+cos^(3)x)sinxdx equals

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  6. If int(3x ^(3)-17)e^(2x)dx={Ax^(3)+Bx^(2)+Cx+D}e^(2x)+k then

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  7. The relation int(sin2x+cos2x)=(1)/(sqrt(2))sin(2x-a)+c is true for

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  8. The value of lambda for which int(4x^(3)+lambda4^(x))/(4^(x)+x^(4))dx=...

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  9. If primitive of sqrt((1+secx)) is 2fog(x)=c, then

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  10. Let f(0)=f(0)=0 and f^(primeprime)(x)=sec^4x+4 then

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  11. If intsec2x dx=f{g(x)}+c then

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  12. If inttan^(4)xdx=Atan^(3)x+Btanx+phi(x), then

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  13. If primitive of sin (log x) is f(x)*{sin g(x)- cos h(x)}+c, (c being c...

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  14. If int cos^(-1)x+cos^(-1)sqrt(1-x^2) dx= Ax+f(x)sin^(-1)x-2sqrt(1-x^2)...

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  15. If int (3x+4)/(x^3-2x-4) \ dx = log|x-2| + k logf(x) + c, then (i) f...

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  16. A primitive of sin 6x is

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  17. If int(sinx)/(sin(x-a))dx=f(x)sina+g(x)cosa+c, then

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  18. If f(x)=int1^x(lnt)/(1+t)dt where x>0, then the values of of x satisfy...

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  19. The value of int0^oo(x dx)/((1+x)(1+x^2)) is equal to

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  20. Let f(x)=int(0)^(x)(sint)/(t)dt(x gt 0) then f(x) has (n in N)

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