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Definite Integration question

2024 · 4 Apr · Shift 1 · Q52

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JEE Main
Mathematics
Definite Integration
2024 · 4 Apr · Shift 1 · Q52

Definite Integration question

2024 · 4 Apr · Shift 1 · Q52

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

If the shortest distance between the lines

\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}

and

\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}

is

\frac{38}{3 \sqrt{5}} \mathrm{k}

, and

\int\limits_0^{\mathrm{k}}\left[x^2\right] \mathrm{d} x=\alpha-\sqrt{\alpha}

, where

[x]

denotes the greatest integer function, then

6 \alpha^3

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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