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Evaluate each of the following integral:...

Evaluate each of the following integral: `int_2^4x/(x^2+1)dx`

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`int_2^4x/(x^2+1)dx`
`=1/2 int_2^4 (2x dx)/(x^2 + 1)`
`=1/2 [log9x^2 + 1]_2^4 + c`
`1/2 [log (16+1) - log (4+1)] + c`
=1/2 log (17/5) + c`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate each of the following integral: inte^(e^2)1/(xlogx)dx

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  2. Evaluate each of the following integral: inte^(pi//2)e^x(sinx-cos x)dx

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  3. Evaluate each of the following integral: int2^4x/(x^2+1)dx

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  4. If int0^1(3x^2+2x+k)dx=0, find the value of kdot

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  5. If int0^a3x^2dx=8,\ write the value of ' a^(prime)dot

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  6. If (x)=int0^x tsint\ dt ,\ then write the value of f^(prime)(x)

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  7. If int0^a1/(4+x^2)dx=pi/8 , find the value of adot

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  8. The value of int-2^2 (ax^3+bx+c)dx depends on (A) the value of b (B) t...

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  9. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  10. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  11. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  12. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  13. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  14. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  15. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  16. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  17. The value of int0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(s in x))dx is ...

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  18. int0^(pi/2) 1/(1+sinx)dx equals 0 b. 1//2 c. 2 d. 3//2

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  19. int0^oo1/(1+e^x)dx equals a. log2-1 b. log2 c. log4-1 d. log2

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  20. The value of int0^(2pi)sqrt(1+sin (x/2)dx is 0 b. 4 c. 2 d. 8

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