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Definite Integration · 2024 · 31 Jan · Shift 1

3 Mathematics questions from this JEE Main paper

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2024 · 31 Jan · Shift 1
Mathematics
Definite Integration

Definite Integration · 2024 · 31 Jan · Shift 1

3 Mathematics questions from this JEE Main paper

Q54.If the integral $525 0 \int \frac{π}{2} sin 2 x cos^{\frac{11}{2}} x (1 + cos^{\frac{5}{2}} x)^{\frac{1}{2}} d x$ is equal to $(n 2 - 64)$ , then $n$ is equal to .
Mathematics · Definite Integration · Numerical
Q55.Let $S = (- 1, \infty)$ and $f : S \to R$ be defined as $f (x) = \int_{- 1}^{x} (e^{t} - 1)^{11} (2 t - 1)^{5} (t - 2)^{7} (t - 3)^{12} (2 t - 10)^{61} d t,$ Let $p =$ Sum of squares of the values of $x$ , where $f (x)$ …
Mathematics · Definite Integration · Numerical
Q60.Let $f : R \to R$ be a function defined by $f (x) = \frac{4 ^{x}}{4 ^{x} + 2}$ and $M = \int_{f (a)}^{f (1 - a)} x sin^{4} (x (1 - x)) d x, N = \int_{f (a)}^{f (1 - a)} sin^{4} (x (1 - x)) d x; a e q \frac{1}{2}$ . If $α M = β N, α, β \in N$ …
Mathematics · Definite Integration · Numerical