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Definite Integration · 2024 · 30 Jan · Shift 2

4 Mathematics questions from this JEE Main paper

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JEE Main
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2024 · 30 Jan · Shift 2
Mathematics
Definite Integration

Definite Integration · 2024 · 30 Jan · Shift 2

4 Mathematics questions from this JEE Main paper

Q31.Let $f : R \to R$ be a function defined by $f (x) = \frac{x}{( 1 + x ^{4} ) ^{1/4}}$ , and $g (x) = f (f (f (f (x))))$ . Then, $18 \int_{0}^{25} x^{2} g (x) d x$ is equal to
Mathematics · Definite Integration · MCQ
Q33.Let $y = f (x)$ be a thrice differentiable function in $(- 5, 5)$ . Let the tangents to the curve $y = f (x)$ at $(1, f (1))$ and $(3, f (3))$ make angles $π /6$ and $π /4$ , respectively with positive $x$ -axis. If $27 1 \int 3 ((f^{'} (t))^{2} + 1) f^{''} (t) d t = α + β 3$ …
Mathematics · Definite Integration · MCQ
Q39.Let $a$ and $b$ be real constants such that the function $f$ defined by $f (x) = {x^{2} + 3 x + a b x + 2, x \leq 1, x > 1$ be differentiable on $R$ . Then, the value of $\int_{- 2}^{2} f (x) d x$ …
Mathematics · Definite Integration · MCQ
Q40.Let $f : R \to R$ be defined as $f (x) = a e^{2 x} + b e^{x} + c x$ . If $f (0) = - 1, f^{'} (lo g_{e} 2) = 21$ and $\int_{0}^{l o g_{e} 4} (f (x) - c x) d x = \frac{39}{2}$ , then the value of $∣ a + b + c ∣$ equals
Mathematics · Definite Integration · MCQ