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int(sin((pi)/(4)-x)dx)/(2+sin2x)=A tan^(...

`int(sin((pi)/(4)-x)dx)/(2+sin2x)=A tan^(-1)(f(x))+B`, where A, B are contants. Then the range of Af(x) is

A

`[-1,1]`

B

`[-sqrt2,sqrt2]`

C

`[0,1]`

D

`[-1,0]`

Text Solution

Verified by Experts

The correct Answer is:
A
`(1)/(sqrt2)int(d(Sinx+cosx))/((sinx+cosx)+1)=(1)/(sqrt2)tan^(-1)(sinx+cosx)+B`
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CENGAGE-INDEFINITE INTEGRATION-Single Correct Answer Type
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  2. int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(1+sqrtx)^(alpha))-(1)/(beta(1+...

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  4. If sqrt(x+sqrt(x^(2)+x))dx=A{x+sqrt(x^(2)+2)}^(3//2)+(B)/(sqrt(x+sqrt(...

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  5. int(x^(2)+1)/(xsqrt(x^(2)+2x-1)sqrt(1-x^(2)-x))dx is equal to

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  6. int(dx)/(x^(2)sqrt(16-x^(2))) has the value equal to

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  7. If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3))+xtan^(2)x+tanx)=Ktan^(...

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  8. int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

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  9. int(3x^(2)+2x)/(x^(6)+2x^(5)+x^(4)+2x^(3)+2x^(2)+5)dx=

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  10. int(1)/((1+sqrtx)sqrt(x-x^(2)))dx is equal to

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  11. If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0), and f...

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  12. If I=int(dx)/(x^(4)sqrt(a^(2)+x^(2))), then I equals

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  13. If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C, then f(x) is eq...

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  14. int(x^(2)(1-logx))/((logx)^(4)-x^(4))dx equals

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  15. int(x(x-1))/((x^(2)+1)(x+1)sqrt(x^(3)+x^(2)+x))=(1)/(2)log|(sqrt(x+(1)...

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  16. int(dx^(3))/(x^(3)(x^(n)+1)) equals

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  17. int((x+1)^(2)x)/(x(x^(2)+1)) is equal to

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  18. int(x^3-x)/(1+x^6)dx is equal to

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  19. int (x^3-1)/((x^4+1)(x+1)) dx is

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  20. The value of int(cos^(3)x)/(sin^(2)x+sinx)dx is equal to

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