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Evaluate the definite integralsint0^(pi/...

Evaluate the definite integrals`int_0^(pi/4 ) (sinxcosx)/(cos^4x+sin^4x)dx`

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To evaluate the definite integral \[ I = \int_0^{\frac{\pi}{4}} \frac{\sin x \cos x}{\cos^4 x + \sin^4 x} \, dx, \] we can start by simplifying the integrand. ...
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NCERT-INTEGRALS-MISCELLANEOUS EXERCISE
  1. Evaluate the definite integralsint(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Integrate the functions(sinx)/(sin(x-a)

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  20. Integrate the functions1/(x^(1/2)+x^(1/3))[Hint: 1/(x^(1/2)+x^(1/3))=1...

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