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Prove that following: underset(0)overs...

Prove that following:
`underset(0)overset(9)intf(x) dx, where f(x) = {:{(sinx, if 0 le x le (pi)/(2)),(1,ifpi/2le x le 3),(e^(x-3), if 3 le x le 9)`

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MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Prove that following: underset(-1)overset(1)int(x-[x])dx

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  2. Prove that following: underset(1)overset(4)intf(x)dx, where f(x) ={ ...

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  3. Prove that following: underset(0)overset(9)intf(x) dx, where f(x) = ...

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  4. Evaluate: underset(0)overset(pi)int(xtanx)/(secx+cosx)dx

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  5. Evaluate: underset(0)overset(pi//2)intlog |sinx|dx

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  6. Evaluate: underset(0)overset(pi//2)intlog|cosx|dx

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  7. Evaluate: underset(0)overset(pi//2)int log tan x dx

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  8. Evaluate the following integrals: int(3ax)/(b^2+c^2x^2)dx

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  9. Evaluate the following integrals: int (x^(2))/(x^(2)+3x+3)dx

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

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  11. Evaluate the following integrals: int(sqrt(1+x^2))/(x^4)dx

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  12. Evaluate the following integrals: int(sin^-1x)/((1-x^2)^(1//2))dx

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  13. Evaluate the following integrals : int(sin^(6)x+cos^(6)x)/(sin^(2)xcos...

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  14. Find: int(sqrtx)/(sqrt(a^3-x^3))

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  15. Evaluate the following integrals: underset(pi//3)overset(pi//2)intsq...

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  16. Evaluate the following integrals: underset(-pi//4)overset(pi//4)int ...

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  17. Evaluate the following integrals: underset(0)overset(pi//2)int(tanx)...

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  18. Evaluate the following integrals: int e^(x) (tanx+1)sec xdx

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  19. Evaluate the following integrals: int 1/(x^(2)-9)dx

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  20. Evaluate: underset(e ) overset(e^2)int(dx)/(xlogx)

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