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If kint(0)^(1)xf(3x)dx=int(0)^(3)tf(t)dt...

If `kint_(0)^(1)xf(3x)dx=int_(0)^(3)tf(t)dt`, then the value of k is

A

9

B

3

C

`1/9`

D

`1/3`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=kint_(0)^(1)xf(3x)dx`
Put 3x=t
`rArrdx=(dt)/(3)`
`thereforel=kint_(0)^(3)(t)/(3)*f(t)*(dt)/(3)=(k)/(9)int_(0)^(3)t*f(t)dt`
Now `(k)/(9)int_(0)^(3)t*f(t)dt=int_(0)^(3)t*f(t)dt` [ Given]
`rArr(k)/(9)=1rArrk=9`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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  2. The value of int (0)^(12a) (f(x))/(f(x)+f(12a-x))dx is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. The value of int(e^(-1))^(e) (dt)/(t(t+1)) is equal to

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