Let S n be the area of the figure enclosed by a curve y = x 2 ( 1 − x ) n ( 0 ≤ x ≤ 1 ) and x-axis, if lim n → ∞ ∑ k = 1 n S k = A 1 , then 'A' is equal to -

Question

Let S n ​ be the area of the figure enclosed by a curve y = x 2 ( 1 − x ) n ( 0 ≤ x ≤ 1 ) and x-axis, if lim n → ∞ ​ ∑ k = 1 n ​ S k ​ = A ​ 1 ​ , then 'A' is equal to -

TestHub · Accepted Answer

S n ​ = ∫ 0 1 ​ x 2 ( 1 − x ) n d x . n = 1 ∑ ∞ ​ ( 1 − x ) n = x 1 − x ​ . n = 1 ∑ ∞ ​ S n ​ = ∫ 0 1 ​ x ( 1 − x ) d x = 2 1 ​ − 3 1 ​ = 6 1 ​ . A ​ 1 ​ = 6 1 ​ , A = 36. ​

Mathematics - Area Under Curves Question with Solution | TestHub

Doubts & Discussion