Nilai ^1 0∫ 5x(1-x)^6 dx = … A. 75/56 B. 10/56 C. 5/56 D. -7/56 E. -10/56

Gunakan parsial.

misal :
u = 5x
du = 5 dx

dv = (1 – x)^6 dx
dv = (1 – x)^6 d(1 – x)/-1 (-1 dari turunan 1 – x)
dv = -(1 – x)^6 d(1 – x)
v = -1/7 (1 – x)^7

= uv -∫v du
= (5x)(- 1/7 (x – 1)^7) – ∫(-1/7 (1 -x)^7 .5 dx
= -5/7x (x – 1)^7 + ∫5/7 (1 – x)^7 dx
= -5/7x (x – 1)^7 + ∫5/7 (1 – x)^7 d(1 – x)/-1
= -5/7 x (x – 1)^7 – ∫5/7 (1 – x)^7 d(1 – x)
= -5/7 x (x – 1)^7 – (5/7)/8 (1 – x)^8
= -5/7 x (x – 1)^7 – 5/56 (1 – x)^8

masukan nilai x

= (-5/7(1) . (1 – 1)^7 – 5/6 (1 – 1)^8) – (5/7 (0) . (0 – 1)^7 – 5/6 (0 – 1)^8)
= 0 – (-5/6 (0 – 1)^8)
= -(-5/6(1))
= -(-5/6)
= 5/6 satuan luas
= C.