Let [t] denote the largest integer less than or equal to t. If \int_{0}^{3} ( [x^2] + [\frac{x^2}{2}] ) \dx=a+b \sqrt{2}-\sqrt{3}-\sqrt{5}+c \sqrt{6}-\sqrt{7}, where a, b, c \in z, then a+b+c is equal to ______. [6 Apr 2024 Shift 2]

JEE Main 6 Apr 2024 Shift 2 Solved Paper

Section: Mathematics

Question : 24 of 90

Marks: +1, -0

Let [t] denote the largest integer less than or equal to t. If

∫

([x2]+[‌

])‌dx=a+b√2−√3−√5+c√6−√7,
where a,b,c∈z, then a+b+c is equal to ______.

[6 Apr 2024 Shift 2]

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