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Let f:RtoR be a differentiable function ...

Let `f:RtoR` be a differentiable function such that `f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt`.
`f(x)` increases for

A

`xgt1`

B

`xlt-2`

C

`xgt2`

D

none of these

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The correct Answer is:
B
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CENGAGE-DEFINITE INTEGRATION -Exercise (Comprehension)
  1. y=f(x) satisfies the relation int(2)^(x)f(t)dt=(x^(2))/2+int(x)^(2)t^(...

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  2. y=f(x) satisfies the relation int(2)^(x)f(t)dt=(x^(2))/2+int(x)^(2)t^(...

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  3. Let f:RtoR be a differentiable function such that f(x)=x^(2)+int(0)^(x...

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  4. Let f:RtoR be a differentiable function such that f(x)=x^(2)+int(0)^(x...

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  5. Let f(x) be a differentiable function such that f(x)=x^2 +int0^x e^-t ...

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  6. f(x) satisfies the relation f(x)-lambdaint0^(pi//2)sinx*costf(t)dt=si...

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  7. f(x) satisfies the relation f(x)-lamda int(0)^(pi//2)sinxcostf(t)dt=si...

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  8. f(x) satisfies the relation f(x)-lambdaint0^(pi//2)sinx*costf(t)dt=si...

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  9. Let f(x) and phi(x) are two continuous function on R satisfying phi(x)...

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  10. Let f(x) and phi(x) are two continuous function on R satisfying phi(x)...

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  11. Let f(x) and phi(x) are two continuous function on R satisfying phi(x)...

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  12. Let f(x) and phi(x) are two continuous function on R satisfying phi(x)...

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  13. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  14. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  15. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  16. Evaluating integrals dependent on a parameter: Differentiate I with ...

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  17. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The range of f(x) is

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  18. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt f(x) is not invertibl...

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  19. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The value of int(0)^(...

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  20. Let u=int0^oo (dx)/(x^4+7x^2+1 and v=int0^x (x^2dx)/(x^4+7x^2+1) then

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