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Prove that underset(0)overset(pi//2)sqrt...

Prove that `underset(0)overset(pi//2)sqrt(costheta) sin^3 theta d theta = (8)/(21)`

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Evaluate the following: underset0 overset(pi//2) int sqrt(costheta sin^3theta dtheta) .

underset0 overset(pi//2)int (sintheta)/sqrt(1+costheta) d theta

Evaluate the following integrals by changing the limits of integration after suitable subsitutions: underset(0)overset(pi//0) (1-cos 3 theta) sin 3 theta d theta

underset0overset(pi//2)int sin^3xdx

Evaluate the following integrals by changing the limits of integration after suitable subsitutions: underset(0)overset(pi)int5(5-4cos theta)^(1//4) sin theta d theta

Prove that underset0overset(pi//2)int log(sintheta)dtheta=underset0overset(pi//2)int log(costheta)dtheta=-pi/2 log2 .

Evaluate int_(0)^(pi//2) cos theta tan ^(-1) ( sin theta)d theta .

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MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Prove that underset(0)overset(pi//2)sqrt(costheta) sin^3 theta d theta...

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  2. For the following (1-4) different results,Write the corresponding inte...

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  3. For the following (1-4) different results,Write the corresponding inte...

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  4. For the following (1-4) different results,Write the corresponding inte...

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  5. For the following (1-4) different results,Write the corresponding inte...

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  6. For the following (1-4) different results,Write the corresponding inte...

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  7. For the following (1-4) different results,Write the corresponding inte...

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  8. For the following (5-7) different results,Write the corresponding inte...

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  9. For the following (5-7) different results,Write the corresponding inte...

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  10. For the following (5-7) different results,Write the corresponding inte...

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  11. Find an anti derivative (or integral) of the following functions by th...

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  12. Write an anti derivative for each of the following functions using the...

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  13. Find an anti derivative (or integral) of the following functions by th...

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  14. Find an anti derivative (or integral) of the following functions by th...

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  15. write down the integrals of the following (9-15) : x^4+x^-5

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  16. write down the integrals of the following (9-15) : 1/x*x !=0

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  17. write down the integrals of the following (9-15) : x+1/x*x !=0

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  18. Find the following integrals: int (x^(2/3) +1)dx

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  19. write down the integrals of the following (9-15) : (3/sqrtx+5x^4) .

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  20. write down the integrals of the following (9-15) : cos2x

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  21. Find the following integrals: int (sinx+cosx)dx

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