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int (0)^(3) (3x+1)/(x^(2)+9) dx =...

` int _(0)^(3) (3x+1)/(x^(2)+9) dx = `

A

`log(2sqrt(2))+pi/12`

B

`log(2sqrt(2))+pi/2`

C

` log (2sqrt(2)) +pi/6`

D

` log (2sqrt(2))+pi/3`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(0)^(3)(3x+1)/(x^(2)+9)dx=(3)/(2)int_(0)^(3)(2x)/(x^(2)+9)dx+int_(0)^(3)(dx)/(x^(2)+9)`
`=[(3)/(2)log(x^(2)+9)+(1)/(3)tan^(-1)((x)/(3))]_(0)^(3)`
`=(3)/(2)(log18-log9)+(1)/(3)((pi)/(4))`
`=(3)/(2)log2+(pi)/(12)=log(2sqrt2)+(pi)/(12)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. The value of int (2)^(4) { |x-2|+|x-3|} dx is

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  2. int (-1)^(2) |x|^(3) dx is equal to

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  3. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  4. int (0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) thet...

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  5. The value of the integral int (-a)^(a) (xe^(x^(2)))/(1+x^(2)) dx is

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  6. int (-pi//2)^(pi//2) (dx)/(1+cosx) is equal to

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  7. The value of int (0)^(12a) (f(x))/(f(x)+f(12a-x))dx is

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  8. If kint(0)^(1)xf(3x)dx=int(0)^(3)tf(t)dt, then the value of k is

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  9. lim(nto oo)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2...

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  10. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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  11. Evaluate: ("lim")(nvecoo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt...

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  12. If f(x) = tanx-tan ^(3) x + tan^(5) x - tan ^(7) x + ... infty for o...

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  13. The value of int(0)^((pi)/(8))cos^(3)4 theta d theta is equal to -

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  14. int (0)^(pi//3) (cos x + sin x)/(sqrt(1+sin 2x))dx is equal to

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  15. int (0)^(1) x^(3//2) sqrt(1-x) dx is equal to

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  16. The value of int (1)^(2) (dx)/((x+1) sqrt((x^2)-1)) is

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  17. If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

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  18. int (-1)^(1) (e^(x^(3)) +e^(-x^(3))) (e^(x)-e^(-x)) dx is equal to

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  19. underset(n to oo)lim((1)/(n)+(1)/(n+1)+...+(1)/(3n)) is equal to

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  20. Let f (x) = x – [x], for every real number x, where [x] is the greates...

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