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Definite Integration question

2022 · 30 Jun · Shift 1 · Q37

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JEE Main
Mathematics
Definite Integration
2022 · 30 Jun · Shift 1 · Q37

Definite Integration question

2022 · 30 Jun · Shift 1 · Q37

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

f(t) = \int\limits_0^t {{e^{{x^3}}}\left( {{{{x^8}} \over {{{({x^6} + 2{x^3} + 2)}^2}}}} \right)dx}

. If

f(1) + f'(1) = \alpha e - {1 \over 6}

, then the value of 150

\alpha

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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