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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Let ∫ x x · ^3 x dx = (1)/(2)(x · f(x) - g(x)) + k , then :

Let ∫xsin⁡x⋅sec⁡3xdx=12(x⋅f(x)−g(x))+k\int x \sin x \cdot \sec^3 x dx = \frac{1}{2}(x \cdot f(x) - g(x)) + k, then :

Options

  1. Af(x)∉(−1,1)f(x) \notin (-1, 1)
  2. Bg(x)=sin⁡xg(x) = \sin x has 6 solution for x∈[−π,2π]x \in [-\pi, 2\pi]
  3. Cg′(x)=f(x),∀x∈Rg'(x) = f(x), \forall x \in R
  4. Df(x)=g(x)f(x) = g(x) has no solution

Correct answer

A. f(x)∉(−1,1)f(x) \notin (-1, 1)

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