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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)e^(-t^(3)).f(x-t^(3))dt`. Then find `f(x)`.

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To solve the problem, we need to find the function \( f(x) \) that satisfies the equation: \[ f(x) = x^2 + 3 \int_0^x e^{-t^3} f(x - t^3) \, dt \] ### Step 1: Define the equation We start with the given equation and label it as Equation (1): ...
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CENGAGE ENGLISH-DEFINITE INTEGRATION -JEE ADVANCED
  1. Let f:RtoR be a differntiable function satisfying f(x)=x^(2)+3int(0)^(...

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  2. Let f be a non-negative function defined on the interval [0,1]. If int...

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  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

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  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  5. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

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  6. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)for...

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  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  8. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

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  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

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  11. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

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  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

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  13. about to only mathematics

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  14. Let S be the area of the region enclosed by y=e^-(x^2),y=0,x=0,a n dx=...

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  15. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

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  16. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

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  17. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

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  18. The option(s) with the values of aa n dL that satisfy the following eq...

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  19. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

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  20. find the period of sin(x/2)-cos(x/3) is

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  21. Let f: Rvec(0,1) be a continuous function. Then, which of the followin...

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