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Integrate the functions (sin^(-1)sqrt(...

Integrate the functions
`(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]`

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Verified by Experts

The correct Answer is:
`(2(2x-1))/(pi)sin^(-1)sqrtx+(2sqrt(x-x^(2)))/(pi)-x+C`
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NCERT TAMIL-INTEGRALS-EXERCISE 7.12
  1. Integrate the functions f'(ax+b)[f(ax+b)]^(n)

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  2. Integrate the functions (1)/(sqrt(sin^(3)xsin(x+alpha)))

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  3. Integrate the functions (sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)s...

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  4. Integrate the functions sqrt((1-sqrtx)/(1+sqrtx))

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  5. Integrate the functions (2+sin2x)/(1+cos2x)e^(x)

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  6. Integrate the functions (x^(2)+x+1)/((x+1)^(2)(x+2))

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  7. Integrate the functions tan^(-1)x

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  8. Integrate the functions (sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4))

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  9. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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  10. Evaluate the definite integrals int(0)^(pi/4)(sinxcosx)/(cos^(4)x+si...

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  11. Evaluate the definite integrals int(0)^((pi)/(2))(cos^(2)xdx)/(cos^...

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  12. Evaluate the definite integrals int((pi)/(6))^((pi)/(3))(sinx+cosx)...

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  13. Evaluate the definite integrals int(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

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  14. Evaluate the definite integrals int(0)^((pi)/(4))(sinx+cosx)/(9+16s...

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  15. Evaluate the definite integrals int(0)^((pi)/(2))sin2xtan^(-1)(sinx...

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  16. Evaluate the definite integrals int(0)^(pi)(xtanx)/(secx+tanx)dx

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  17. Evaluate the definite integrals int(1)^(4)[abs(x-1)+abs(x-2)+abs(x-3...

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  18. Prove the following int(1)^(3)(dx)/(x^(2)(x+1))=(2)/(3)+"log"(2)/(3)

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  19. Prove the following int(0)^(1)xe^(x)dx=1

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  20. Prove the following int(-1)^(1)x^(17)cos^(4)xdx=0

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