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Evaluate: int0^1|5x-3|dx...

Evaluate: `int_0^1|5x-3|dx`

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`I=int_0^1|5x-3|dx`
`I=int_0^(3/5)(-(5x-3))dx+int_(3/5)^(1)(5x-3))dx`
`I=int_0^(3/5)(3-5x)dx+int_(3/5)^(1)(5x-3))dx`
`I=(3x-(5x^2)/2)_0^(3/5)+((5x^2)/2-3x)_(3/5)^1`
`I=(3(3/5)-(5(3/5)^2)/2)+((5(1)^2)/2-3(1))-(5(3/5)^2)/2-3(3/5))`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integrals: int0^(pi//4)(sin^2xcos^2x)/((sin...

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  2. Evaluate the following integrals: int0^(pi//2)(tanx)/(1+m^2tan^2x)d...

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  3. Evaluate: int0^1|5x-3|dx

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

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

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

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

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  8. Evaluate: int0^3[x]dx

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

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

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

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

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

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

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

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

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

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

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

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

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