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int (1/e)^e |logx|dx =...

`int _(1/e)^e |logx|dx` =

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`I=int_(1/e)^e|logx|dx`
`int_(1/e)^e-logxdx+int_(1/e)^elogxdx`
`I=I_1+I_2`
`I_1=-[xlogx-x]_(1/e)^1`
...
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: int0^1|5x-3|dx

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  2. Evaluate: (i) \int(-1)^1f(x)dx ,\where\, f(x)={1-2x ,xlt=0 ;1+2x ,xgt=...

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  3. int (1/e)^e |logx|dx =

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  4. If a >0, find int0^(3a)|x^2-a^2|dxdot

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  5. If [dot] denotes the greatest integer function, then find the valu...

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  6. Evaluate: int0^3[x]dx

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  7. int0^1d/(dx){sin^(-1)((2x)/(1+x^2))}dx is equal to 0 (b) pi (c) ...

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  8. Evaluate the following integrals: int(-a)^a(xe^(x^2))/(1+x^2)dx

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  9. Evaluate the following integrals: int0^(pi//4)|cos2x|dx

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  10. Evaluate the following integrals: int-5^0f(x)dx ,w h e r ef(x)=|x|+|x+...

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  11. Evaluate the following definite integrals (1-58): int1^2 1/(sqrt((x...

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  12. Evaluate the following integrals: int0^picosx|cosx|dx

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  13. Let f(x)=x-[x], for ever real number x ,w h e r e[x] is the g...

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  14. Evaluate: int0^(sqrt(3))1/(1+x^2)sin^(-1)((2x)/(1+x^2))dx

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  15. Evaluate the following integrals: int0^9f(x)dx ,w h e r ef(x)= {s...

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  16. Evaluate the following integrals: int0^2|x^2-3x+2|dx

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  17. Evaluate the following integrals: int0^1((1-x)/(1+x))dx

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  18. Prove that: inta^b(f(x))/(f(x)+f(a+b-x))dx=(b-a)/2

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  19. Evaluate of each of the following integrals (1-15): int0^5root(3)(...

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  20. Evaluate of each of the following integrals (1-15): int(-pi//4)^(p...

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