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Evaluate the definite integralsint0^1 (...

Evaluate the definite integrals`int_0^1 (dx)/(sqrt(1+x)-sqrt(x))`

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To evaluate the definite integral \[ I = \int_0^1 \frac{dx}{\sqrt{1+x} - \sqrt{x}}, \] we will simplify the integrand first. ...
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NCERT-INTEGRALS-MISCELLANEOUS EXERCISE
  1. Integrate the functions(e^x)/((1+e^x)(2+e^x)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Evaluate the definite integralsint0^pi (xtanx)/(secx+tanx)dx

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  17. Evaluate the definite integralsint1^4[|x-1|+|x-2|+|x-3|]dx

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  18. Prove thatint1^3(dx)/(x^2(x+1))=2/3+log2/3

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  19. Prove thatint0^1x e^x dx=1

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  20. Prove thatint0^(pi/4) 2tan^3xdx=1-log2

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