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#### sbhatnagar

##### Active member

- Jan 27, 2012

- 95

Let $f:[1,\infty)\to [2,\infty)$ be a differentiable function such that $f(1)=2$. If

$$ 6\int_{1}^{x} f(t)\, dt+5=3x \, f(x)-x^3$$

for all $x \geq 1$, then:

1) Find the value of $f(2)$.

2) Find $\mathcal{L} \{ f(t)\}$.

$$ 6\int_{1}^{x} f(t)\, dt+5=3x \, f(x)-x^3$$

for all $x \geq 1$, then:

1) Find the value of $f(2)$.

2) Find $\mathcal{L} \{ f(t)\}$.

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