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Prove that underset(-pi//4)overset(pi//4...

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

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MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Evaluate the following: underset(0)overset(pi//2)intsin^3x dx

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

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

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

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  5. Prove that: int(0)^(2pi)cos^(5)x=0

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

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  7. Evaluate the following: underset(-pi//4)overset(pi//4)int|sinx|dx

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  8. Evaluate the following: underset(-pi//2)overset(pi//2)int|sinx|dx

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  9. Evaluate the following: underset(-pi//4)overset(pi//4)intsin^2xdx

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  10. Evaluate the following: underset(-pi//2)overset(pi//2)intsin^2xdx

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  11. Evaluate the following: underset(0)overset(pi/2)intsin^5xdx

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  12. Evaluate the following: underset(-pi//2)overset(pi//2)intsin^7xdx

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  13. Evaluate the following: underset(-pi)overset(pi)intx^(10)(sinx)^7dx

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  14. Evaluate the following: underset(0)overset(pi/2)int(xsinx cosx)/(sin...

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  15. Evaluate the following: underset(0)overset(pi//2)int sin x cos x tan...

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  16. Prove that following: underset(0)overset(pi)int(xtanx)/(secx+cosx)dx...

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  17. Integrate the following: underset(0)overset(pi)int(sinx)/(1+Cos^2x)d...

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  18. Prove that following: underset(0)overset(pi//2)int(sinx-cosx)/(1+sin...

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  19. Integrate the following: underset(0)overset(pi//2)int(Cos^2x)

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  20. Prove that following: underset(0)overset(pi)int(xtanx)/(secx+Tanx)dx...

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