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If f(x) = (1)/(cos^(2)xsqrt(1+tanx)) the...

If f(x) = `(1)/(cos^(2)xsqrt(1+tanx))` then its antiderivative F(x) (given that F(0) = (4) is

A

`sqrt(1+tan x)+4`

B

`(2)/(3) (1 + tan x)^(3//2)`

C

`2(sqrt(1 + tan x)+1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-INDEFINITE INTEGRATION-SOLVED EXAMPLE ( LEVEL 1 ( SINGLE CORRECT ANSWER TYPE QUESTION ))
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  2. If f(x) = (1)/(cos^(2)xsqrt(1+tanx)) then its antiderivative F(x) (giv...

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  3. Let f(x)=1/(4-3cos^2x+5sin^2x) and if its antiderivative F(x)=(1/3) ta...

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  4. Let f(x) = (sqrttanx)/(sinxcosx)andF(x) is its antiderivative , if F(p...

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  5. The value of int (dx)/(x^(4)+5x^(2)+4) is

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  6. int\ ((x-1)^2)/((x^2+1)^2)dx=tan^(- 1)x+g(x)+c then g(x)=

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  7. If int(sin x)/(sin^(2)x+4cos^(2)x)dx=(1)/(sqrt(3))Tan^(-1)((g(x))/(sqr...

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  8. If int(x)/(x^(2)-4x+8)dx=Klog(x^(2)-4x+8)+tan^(-1)((x-2)/(2)) + C then...

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  9. The value of int(dx)/(xsqrt(1-x^(3))) is equal to

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  10. int(cos4x-1)/(cotx-tanx)dx is equal to

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  11. inte^(tan^- 1x)[(1+x+x^2)/(1+x^2)]dx

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  12. int(dx)/sqrt(2-3x-x^(2))=fog(x)+C then

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  13. If int(dx)/(xsqrt(5x^(2)-3))=Ktan^(-1)f(x)+C then

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  14. The value of int(cos2x)/(cosx+sinx)dx is

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  15. If int (cos4x+1)/(cot x - tanx)=Kcos4x+C, then

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  16. inte^(x)(1+sinx)/(1+cosx)dx is equal to

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  17. If intsqrt(1+sec x) dx = K sin^(-1)(f(x)) + C then

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  18. The antiderivative of f (x) = log (log x ) + 1/(log x)^(2) whose graph...

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  19. int(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)(a,bgt0) is equal to

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  20. f(x) = (1//2) (x^(2) - 1)

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