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Definite Integration question

2024 · 6 Apr · Shift 2 · Q52

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JEE Main
Mathematics
Definite Integration
2024 · 6 Apr · Shift 2 · Q52

Definite Integration question

2024 · 6 Apr · Shift 2 · Q52

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

[t]

denote the largest integer less than or equal to

t

. If

\int\limits_0^3\left(\left[x^2\right]+\left[\frac{x^2}{2}\right]\right) \mathrm{d} x=\mathrm{a}+\mathrm{b} \sqrt{2}-\sqrt{3}-\sqrt{5}+\mathrm{c} \sqrt{6}-\sqrt{7}

, where

\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{Z}

, then

\mathrm{a}+\mathrm{b}+\mathrm{c}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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