Mathematics · 2021
JEE Main · 26 February 2021, Shift 2 · Q67
Let f(x)=∫_0^x e^t f( t ) dt + e^x be a differentiable function for all x ∈ R. Then f(x) equals:
Let $\displaystyle f(x)=\int_0^x \mathrm{e}^{\mathrm{t}} f(\mathrm{t}) \mathrm{dt}+\mathrm{e}^x$ be a differentiable function for all $\displaystyle x \in \mathbf{R}$. Then $\displaystyle f(x)$ equals :
Official answer
(1)
$\displaystyle 2 \mathrm{e}^{\left(\mathrm{e}^x-1\right)}-1$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.