o∫1 5x(1 − x)6 dx =...

Integral Tertentui

₀¹∫ 5x(1 - x)⁶ dx =
.
misal u = 1- x --> x= 1- u
du/dx = -1 --> dx = - du
batas intergral
x = 0 --> u = 1-0 = 1
x = 1 --> u = 1-1 = 0

₀¹∫ 5x(1-x)⁶  dx = ₁⁰∫ 5(1-u)(u)⁶ (- du)
=  -5 .   ₁⁰∫  u⁶ - u⁷ du
= - 5 [ 1/7 u⁷ - 1/8 u⁸]⁰₁
= - 5 [ 1/7 (0⁷-1⁷) - 1/8 (0⁸-1⁸]
= - 5 [ - 1/7 + 1/8]
= - 5 [- 1/56]
= 5/56