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Definite Integration · 2021 · 31 Aug · Shift 1

3 Mathematics questions from this JEE Main paper

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JEE Main
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2021 · 31 Aug · Shift 1
Mathematics
Definite Integration

Definite Integration · 2021 · 31 Aug · Shift 1

3 Mathematics questions from this JEE Main paper

Q23.Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If $\int_{0}^{x} 1 - (f^{'} (t))^{2} d t = \int_{0}^{x} f (t) d t$ , $0 \leq x \leq 1$ and f(0) = 0, then $x \to 0 lim \frac{1}{x ^{2}} \int_{0}^{x} f (t) d t$ …
Mathematics · Definite Integration · MCQ
Q37.Let [t] denote the greatest integer $\leq$ t. Then the value of $8. - \frac{1}{2} \int 1 ([2 x] + ∣ x ∣) d x$ is .
Mathematics · Definite Integration · Numerical
Q43.If $x ϕ (x) = 5 \int x (3 t^{2} - 2 ϕ^{'} (t)) d t$ , x > $-$ 2, and $ϕ$ (0) = 4, then $ϕ$ (2) is .
Mathematics · Definite Integration · Numerical