Slicing a Trapezoid
Difficulty: Medium · Topics: Calculus, Integration, Riemann Sums
Trapetsiyani kesmalarga bo‘lish
In the trapezoid ABCD we have overlineAB=6, overlineBC=5, overlineAD=3 and angle B=90^°, with AD parallel to BC.
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The points dividing the side AB into n equal parts are B 1, B 2, B 3, …, B n-1, taken in order starting from A, and through each of them a line is drawn parallel to BC, meeting the side CD at C 1, C 2, C 3, …, C n-1 respectively. Writing B n=B and C n=C, find the value of
lim n→∞3/nΣ k=1^noverlineB kC k^ 2.
ABCD trapetsiyada overlineAB=6, overlineBC=5, overlineAD=3 va angle B=90^°, AD esa BC ga parallel.
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AB tomonni n ta teng qismga bo‘luvchi nuqtalar A dan boshlab tartib bilan B 1, B 2, B 3, …, B n-1 deb olingan va ularning har biridan BC ga parallel to‘g‘ri chiziq o‘tkazilgan; bu chiziqlar CD tomonni mos ravishda C 1, C 2, C 3, …, C n-1 nuqtalarda kesadi. B n=B va C n=C deb, quyidagining qiymatini toping:
lim n→∞3/nΣ k=1^noverlineB kC k^ 2.