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Definite Integration · 2025 · 2 Apr · Shift 2

3 Mathematics questions from this JEE Main paper

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JEE Main
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2025 · 2 Apr · Shift 2
Mathematics
Definite Integration

Definite Integration · 2025 · 2 Apr · Shift 2

3 Mathematics questions from this JEE Main paper

Q27.Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10 \int_{1}^{1} f (t) dt = 5 x f (x) - x^{5} - 9$ for all $x ⩾ 1$ , then the value of $f (3)$ is :
Mathematics · Definite Integration · MCQ
Q40.Let $(a, b)$ be the point of intersection of the curve $x^{2} = 2 y$ and the straight line $y - 2 x - 6 = 0$ in the second quadrant. Then the integral $I = \int_{a}^{b} \frac{9 x ^{2}}{1 + 5 ^{x}} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q43. $4 \int_{0}^{1} (\frac{1}{3 + x ^{2} + 1 + x ^{2}}) d x - 3 lo g_{e} (3)$ is equal to :
Mathematics · Definite Integration · MCQ