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

Prove that: `int_(0)^(2pi)cos^(5)x=0`

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The correct Answer is:
`(pi)/2`
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By using the properties of definte, prove that int_(0)^(pi//2)cos^(2)x dx=(pi)/4

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int_(0)^(pi//4) cos^(2) x dx

Using property of define integrals, prove that : int_(0)^(pi//2)logcos x dx=(-pi)/2log2

Prove that : int_(0)^(pi/4)(sqrt(tanx)+sqrt(cotx))dx=sqrt(2).pi/2 .

By using the properties of definte, prove that int_(0)^(pi)(e^(cosx))/(e^(cosx)+e^(-cosx))dx=(pi)/2

Evaluate : int_(0)^(2pi) cos^(5)x dx .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=(pi)/4

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BETTER CHOICE PUBLICATION-INTEGRALS-PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. Evaluate the following integrals: int(-pi//4)^(pi//4)sin^(2)x dx

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  2. Evaluate the following integrals: int(-pi//4)^(pi//2)sin^(2)x dx

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

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  4. Evaluate int(0)^(pi)log(1+cosx)dx

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  5. Evaluate the following integrals : int1/(sqrt(x)-x)dx

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  6. Evaluate the following integrals : int 1/ (x-sqrt(x))dx

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  7. Evaluate the following integrals : int 1/(cos^(2)x+2sin^(2)x)dx

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  8. Evaluate the following integrals : int 1/(sin^(2)x+4cos^(2)x)dx

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  9. Evaluate int0^(pi/2) (cosx)/((2+sinx)(3+sinx) ) dx

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  10. Evaluate int0^(pi/2) (cosx)/((3+sinx)(4+sinx) ) dx

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  11. Evaluate the following integrals : int(0)^(pi//2)(cosx)/((4+sinx)(5+...

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  12. Evaluate the following integrals : int(0)^(pi//2)(2sinx+3cosx)/(sinx...

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  13. Using properties of definite integrals, show that int(0)^(pi//2)(xdx...

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  14. Using properties of definite integrals, show that int(0)^(pi//2)(sin...

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  15. Prove that : int0^pi (xtanx)/(secxcosecx)dx =pi^2/4.

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  16. Evaluate: int(5x)/((x+1)(x^(2)-4))dx

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  17. Evaluate the following integrals : intsin^(2)x cos^(2)x dx

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  18. Evaluate the following integrals : int (sin^(3)x)/(cosx)dx

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  19. Evaluate the following integrals : int (cos^(3)x)/(sinx)dx

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  20. Evaluate the following integrals : int (dx)/(e^(x)+3e^(-x))

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