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Prove thatint0^1sin^(-1)xdx=pi/2-1...

Prove that`int_0^1sin^(-1)xdx=pi/2-1`

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To prove that \[ \int_0^1 \sin^{-1} x \, dx = \frac{\pi}{2} - 1, \] we will use integration by parts. ...
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NCERT-INTEGRALS-MISCELLANEOUS EXERCISE
  1. Integrate the functions(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt...

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  2. Prove thatint-1^1x^(17)cos^4x dx=0

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  3. Prove thatint0^1sin^(-1)xdx=pi/2-1

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  4. Integrate the functions(5x)/((x+1)(x^2+9)

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  5. Integrate the functions1/((x^2+1)(x^2+4)

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

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  7. Integrate the functions1/(sqrt((x+a)(x+b))

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  8. Evaluate the definite integralsint0^1 (dx)/(sqrt(1+x)-sqrt(x))

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  9. Evaluate the definite integralsint(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2...

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  10. Evaluate the definite integralsint0^(pi/2)(cos^2x dx)/(cos^2x+4sin^2x...

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  11. Evaluate the definite integralsint0^(pi/4 ) (sinxcosx)/(cos^4x+sin^4x)...

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  12. Evaluate the definite integrals int(pi/2)^pie^x((1-sinx)/(1-cosx))dx

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

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  14. Integrate the functionstan^(-1)sqrt((1-x)/(1+x))

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

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

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  17. Integrate the functionssqrt((1-sqrt(x))/(1+sqrt(x)))

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  18. Evaluate the definite integralsint0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  19. Evaluate the definite integralsint0^(pi/2)sin2xtan^(-1)(sinx)dx

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  20. Choose the correct answersint(cos2x)/((sinx+cosx)^2)dxis equal(A) (-1)...

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