Z 1
0
f(x) dx =
1
3
, then find Z 1
0
(5 − 6f(x)) dx.
Given that ∫₀¹ f(x) dx = 1/3, we need to find ∫₀¹ (5 - 6f(x)) dx.
This can be written as ∫₀¹ 5 dx - 6∫₀¹ f(x) dx
The integral ∫₀¹ 5 dx is simply 5 times the interval [0,1], which equals 5.
Substitute the value of ∫₀¹ f(x) dx = 1/3, we get:
5 - 6(1/3) = 5 - 2 = 3
Therefore, ∫₀¹ (5 - 6f(x)) dx = 3.