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If int cos^(-1)x+cos^(-1)sqrt(1-x^2) dx=...

If `int cos^(-1)x+cos^(-1)sqrt(1-x^2) dx= Ax+f(x)sin^(-1)x-2sqrt(1-x^2)+c` then

A

`f(x)=x`

B

`f(x)=-2x`

C

`A=(pi)/(4)`

D

`A=(pi)/(2)`

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AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (More than one answer)
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  2. If primitive of sin (log x) is f(x)*{sin g(x)- cos h(x)}+c, (c being c...

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

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  5. A primitive of sin 6x is

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

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

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

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  9. If f(x)=int0^x(sint)/t dt ,x >0, then

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  10. The value of int0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is

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  11. inta^b sgn(x)dx equals (a,b in R)

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  12. IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,bn=int0^(pi/2)((sinn x)/(sinx))...

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  13. int0^1 sin(x^2+2x+1)dx-int1^2 sinx^2 dx is equal to (i)0 (ii)1 (ii...

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  14. Ifx=int0^y(dt)/(sqrt(1+9t^2))a n d(d^2y)/(dx^2)=a y ,t h e nfin da

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  15. The integral underset(0)overset(pi)int x f(sinx )dx is equal to

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  16. Let f(x) be an odd continous function which is periodic with period 2....

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  17. If I=overset(4)underset(3)int (1)/(3sqrt(logx))dxthen

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  18. Let f : (0,oo) to R and F(x)=int(0)^(x)t f(t)dt. If F(x^(2))=x^(4)+x...

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  19. Let l(1)=int(1)^(10^(4))({sqrt(x)})/(sqrt(x))dx and l(2)=int(0)^(10)x{...

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  20. If f(x)=x^(2)int(0)^(1)f(t)dt+2, then

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