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The value of overset(pi//2)underset(0)in...

The value of `overset(pi//2)underset(0)int x^(10) sin x" dx"`, is then the value of `mu_(10)+90mu_(8)`, is

A

`10(pi/2)^(3)`

B

`10(pi/2)^(9)`

C

`pi/2`

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `l_(10)=int_(0)^(pi//2)x^(10)sinx dx`
`=[-x^(10)cosx]_(0)^(pi//2)10x^(9).cos xdx`
`=0+[10x^(9)sinx]_(0)^(pi//2)-int_(0)^(pi//2)90x^(8)sin xdx`
`=10((pi)/(2))^(9)-90l_(8)`
`rArr" "l_(10)+90l_(8)=10((pi)/(2))^(9)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. The value of overset(pi//2)underset(0)int x^(10) sin x" dx", is then t...

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  2. If int0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx, then lambda is ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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