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int-1^1 (17x^5-x^4+29x^3-31x+1)/(x^2+1)d...

`int_-1^1 (17x^5-x^4+29x^3-31x+1)/(x^2+1)dx` is equal to

A

`4/5`

B

`5/4`

C

`4/3`

D

`3/4`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int_(-1)^(1)(17x^(5)+29x^(3)-31x)/(x^(2)+1)dx-int_(-1)^(1)(x^(4)-1)/(x^(2)+1)dx`
`=0-2int_(0)^(1)((x^(2)-1)(x^(2)+1))/((x^(2)+1))dx`
`=-2[((x^(3))/(3)-x)]_(0)^(1)=(4)/(3)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. If int0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx, then lambda is ...

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  2. The value of the integral int3^6 sqrtx/(sqrt(9-x)+sqrtx)dx is

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  3. int-1^1 (17x^5-x^4+29x^3-31x+1)/(x^2+1)dx is equal to

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  4. The value of int (0)^(pi//2) (2^(sinx))/(2^(sinx)+2^(cosx))dx is

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  5. Evaluate int0^(pi/4) log(1+tanx)dx

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  6. The value of the integral int (a)^(b) (sqrt(x)dx)/(sqrt(x)+sqrt(1+b-x...

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  7. int (0)^(pi//2) (cos x - sin x)/(1+cos x sin x)dx is equal to

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  8. Evaluate: ("lim")(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/...

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  9. The value of the integral int (0)^(pi//2) log | tan x| dx is

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  10. int (-pi//2)^(pi//2) sin^(4) x cos^(6) x dx is equal to

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  11. If f(x) = f(a+x) and int(0)^(a) f(x) dx = k, "then" int (0)^(na) f(x) ...

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  12. The value of int(0)^(sqrt(2)) [ x^(2)] dx where [*] is the greatest i...

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  13. int0^pi(x dx)/(a^2cos^2x+b^2sin^2x)

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  14. l=int(-2)^(1)(tan^(-1)x+"cot"^(-1)(1)/(x))dx is equal to

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  15. int(0)^(pi) x sin^(4) x dx is equal to

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  16. If int (0)^(pi//2) sin^(6) dx = (5pi)/32 , then the value of int (...

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  17. int (0)^(pi//4) [ sqrt(tan x)+ sqrt(cot x)] dx is equal to

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  18. Evaluate the following limit: lim(nto oo)[(n!)/(n^(n))]^(1//n)

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  19. Let a, b and c be non - zero real numbers such that int (0)^(3) (3ax...

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  20. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

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