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Prove that underset(0)overset(1)intx(1-x...

Prove that `underset(0)overset(1)intx(1-x)^5dx = 1/42`

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MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Evaluate the following integrals: underset(1)overset(3)int(sqrt(4-x)...

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  2. Evaluate the following integrals: underset(0)overset(a)int(sqrtx)/(s...

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  3. Prove that underset(0)overset(1)intx(1-x)^5dx = 1/42

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  4. Evaluate: underset(-1)overset(1)intlog((2-x)/(2+x))dx.

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  5. Evaluate the following integrals: underset(0)overset(pi//2)int(cosx)...

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  6. Evaluate the following integrals: underset(0)overset(pi//2)int(sin^2...

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  7. Evaluate the following integrals: underset(0)overset(pi//2)int(sinx-...

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  8. Evaluate the following integrals: underset(0)overset(pi//2)int(sinx)...

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  9. Evaluate the following integrals: underset(0)overset(pi)int(x)/(1+si...

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  10. Evaluate the following integrals: underset(0)overset(pi)int(x)/(a^2c...

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  11. Evaluate the following integrals: underset(0)overset(1)int(log(1+x))...

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  12. Evaluate the following integrals: underset(-pi//2)overset(pi//2)int(...

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  13. Evaluate the following integrals: underset(-8)overset(8)int(sin^(93)...

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  14. Evaluate the following integrals: underset(-1)overset(1)intsin^5 x c...

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  15. Evaluate the following integrals: underset(-pi//4)overset(pi//4)intx...

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  16. Evaluate the following integrals: underset(-1)overset(1)intx^(17) co...

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  17. Evaluate the following: underset(0)overset(pi//2)intsin^3x dx

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  18. Evaluate the following: underset(0)overset(pi/2)intcos^2x dx

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  19. Prove that underset(-pi//4)overset(pi//4)intsin^2x dx = pi/4 - 1/2

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  20. Prove that underset(-pi//4)overset(pi//4)intcos^2x dx = pi/4+1/2

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