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Let f:RtoR be a differntiable function s...

Let `f:RtoR` be a differntiable function satisfying `f(x)=x^(2)+3int_(0)^(x^(1/3))e^(-t^(3)).t^2.f(x-t^(3))dt`. Then find `f(x)`.

A

`1/3`

B

`1/4`

C

`7/12`

D

`5/12`

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The correct Answer is:
D
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VK JAISWAL-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let f:RtoR be a differntiable function satisfying f(x)=x^(2)+3int(0)^(...

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  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

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  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

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  4. int( (x^2+1)dx)/x

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  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

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  6. int( x^2+3)/(x^2+2)dx

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  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

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  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

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  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

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  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

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  11. Find the value of |a| for which the area of triangle included between ...

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  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

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  13. int( x^3)/(x^2-3)dx

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  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

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  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

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  16. int( x^3)/(x^2-2)dx

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  17. IF M be the maximum valur of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

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  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

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  19. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

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  20. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

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  21. Given a funtion g, continous everywhere such that g (1)=5 and int (0)^...

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