1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider, f ( x )=| x 3-4 x sin x - tan x sec 2 x 3 a 2+1 2 a a 6+6 a + k 1 2|. If ∫ limits(-π/4)(π/4) f(x) d x ≥ 0 ∀ a ∈ R then number of integral values of k is(are) -

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Q. Consider, $f ( x )=\begin{vmatrix} x ^3-4 x & \sin x -\tan x & \sec ^2 x \\ 3 a ^2+1 & 2 a & a ^6+6 \\ a + k & 1 & 2\end{vmatrix}$. If $\int\limits_{\frac{-\pi}{4}}^{\frac{\pi}{4}} f(x) d x \geq 0 \forall a \in R$ then number of integral values of $k$ is(are) -

Integrals

Solution:

Correct answer is (d) 3