Let f(x)=∫₀ˣ eᵗ f(t) dt + eˣ be a... | Differential Equations

JEE MAIN 2021

26.02.21_S2

Question

Let $f(x)=\int_0^x e^t f(t) d t+e^x$ be a differentiable function for all $x \in R$. Then $f(x)$ equals :

Select the correct option:

$2 \mathrm{e}^{\left(\mathrm{e}^{\mathrm{x}}-1\right)}$

$e^{e^x}-1$

$2 e^{e^x}-1$

$e^{\left(e^x-1\right)}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

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