Areas Under a Fading Cosine

Difficulty: Medium · Topics: Calculus, Integration, Series

So‘nib boruvchi kosinus ostidagi yuzalar

For each natural number n, let S n be the area of the figure enclosed by the curve y=≤ft(1/2 )^ncos x and the x-axis on the closed interval ≤ft[(n-1)/(2)π,\ n/2π ].

If Σ n=1^∞S n=α, what is the value of 100α?

Har bir natural n son uchun S n — ≤ft[(n-1)/(2)π,\ n/2π ] yopiq oraliqda y=≤ft(1/2 )^ncos x egri chiziq va x o‘qi bilan chegaralangan shakl yuzi bo‘lsin.

Agar Σ n=1^∞S n=α bo‘lsa, 100α ning qiymati nechaga teng?