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The value of int (0)^(12a) (f(x))/(f(x)...

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

A

a

B

2a

C

3a

D

6a

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l =int_(0)^(12a)(f(x))/(f(x)+f(12a-x))dx` … (i)
`rArrl=int_(0)^(12a)(f(12a-x))/(f(12a-x)+f(x))dx` … (ii)
On adding Eqs . (i) and (ii) , we get
`2l=int_(0)^(12a)1dx=[x]_(0)^(12a)`
`rArrl=6a`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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  6. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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

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

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

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

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

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

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  17. The value of int (0)^(1) (x^(4) +1)/(x^(2)+1)dx is

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  18. The value of overset(5)underset(3)int (x^(2))/(x^(2)-4)dx, is

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  19. The value of int (0)^(pi//2) ((sin x + cos x)^(2))/(sqrt(1+sin 2x) dx...

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  20. int (0)^(a) sqrt(a^(2) - x^(2)) dx is equal to

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