Mathematics · 2021
JEE Main · 27 July 2021, Shift 2 · Q86
If ∫_0^π( sin^3 x) e^- sin^2 x d x=α-(β)/e ∫_0^1 √ t e^t dt, then α+β is equal to \ \ \ \.
If $\displaystyle \int_0^\pi\left(\sin ^3 x\right) \mathrm{e}^{-\sin ^2 x} \mathrm{~d} x=\alpha-\frac{\beta}{\mathrm{e}} \int_0^1 \sqrt{\mathrm{t}} \mathrm{e}^{\mathrm{t}} \mathrm{dt}$, then $\displaystyle \alpha+\beta$ is equal to \_\_\_\_.
Official answer
5
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.