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Evaluate the following: int(-pi/2)^(pi...

Evaluate the following:
`int_(-pi/2)^(pi/2)sin^7xdx`

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Verified by Experts

`sin^7(-x) = (-sinx)^7 = -sin^7x`
therefore `sin^7x` is an odd function
therefore `int_(-pi/2)^(pi/2) sin^7 x dx` = 0
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A N EXCEL PUBLICATION-INTEGRALS-QUESTION BANK
  1. Using properties evaluate the following definite integrals, evaluate ...

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  2. Evaluate:int0^pix/(1+sinx)dx

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  3. Evaluate the following: int(-pi/2)^(pi/2)sin^7xdx

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  4. Using properties evaluate the following definite integrals, evaluate ...

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  5. Using properties evaluate the following definite integrals, evaluate...

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  6. Evaluateint0^pilog(1+cosx)dx

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  7. Using properties evaluate the following definite integrals, evaluate ...

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  8. Using properties evaluate the following definite integrals, evaluate...

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  9. Show that int0^a f(x) g(x) d x=2 int0^a f(x) d x, if f and g are defin...

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  10. Choose the correct answer int(-pi/2)^(pi/2) (x^3+x cosx+tan^5 x+1) dx ...

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  11. Choose the correct answer int0^(pi/2) log((4+3sinx)/(4+3cosx)) dx

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  12. Evaluate int-1^1 sin^5x cos^4x dx

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  13. Evaluate int(pi/6)^(pi/3) dx/(1+sqrttanx)

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  14. Find int0^(pi/2) logsinxdx

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  15. Integrate the following functions w.r.t.x (e^(5logx) - e^(4logx))/(e^(...

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  16. Integrate the following functions w.r.t.x cosx/sqrt(4-sin^2x)

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  17. Integrate the following functions x^3/sqrt(1-x^8)

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  18. integrate the following functions e^x/((1+e^x)(2+e^x))

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  19. Integrate the following: tan^-1sqrt((1-x)/(1+x))

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  20. Evaluate the following definite integrals: int0^pi (xtanx)/(secx+tanx)...

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