Let α = ∫₀^∞ 1/(1 + t²) dt Which of the following is true?मान लीजिए α = ∫₀^∞ 1/(1 + t²) dt
Let α = ∫₀^∞ 1/(1 + t²) dt
Which of the following is true?
मान लीजिए α = ∫₀^∞ 1/(1 + t²) dt
निम्नलिखित में से कौन-सा सत्य है?
Show answerHide answer
Correct answer: (C) sin(α) = 1sin(α) = 1
Explanation
α = tan⁻¹(∞) − tan⁻¹(0) = π/2, a constant. So dα/dt = 0, α is irrational, and sin(π/2) = 1.α = tan⁻¹(∞) − tan⁻¹(0) = π/2 एक अचर है। अतः dα/dt = 0, α अपरिमेय है और sin(π/2) = 1 है।