The least value of n (n ∈ ℕ) , such that the function f(n, x) = ∫ ncos (nx)dx satisfies f(n, (π)/(2)) = -1 , is (given, f(n, 0) =0 )

Correct answer: A. 3 Given function is f(n, x) = n ⋅ ( (nx))/(n) + c As f (n, 0) = 0 ⇒ c = 0 ∴ f(n, x) = (nx) If f(n, (π)/(2)) = - 1 , we have ((nπ)/(2)) = - 1 ⇒ n = 3, 7, 11, ∴ n _ = 3

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Indefinite Integration

NTA Abhyas 2020 · Mathematics · Indefinite Integration

The least value of n (n ∈ ℕ) , such that the function f(n, x) = ∫...

The least value of

n \left(n \in \mathbb{N}\right)

, such that the function

f\left(n, x\right) = ∫ ncos \left(nx\right)dx

satisfies

f\left(n, \dfrac{\pi}{2}\right) = -1

, is (given,

f\left(n, 0\right) =0

)

Options

A $3$
B $4$
C $5$
D $6$

Correct answer

A. $3$

Step-by-step solution

Given function is

f\left(n, x\right) = n ⋅ \dfrac{\sin \left(nx\right)}{n} + c

f \left(n, 0\right) = 0 ⇒ c = 0

∴ f\left(n, x\right) = \sin \left(nx\right)

f\left(n, \dfrac{\pi}{2}\right) = -

, we have

\sin \left(\dfrac{n\pi}{2}\right) = -

1

⇒ n = 3, 7, 11, \ldots \ldots

∴ {n}_\min = 3

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