A Function Symmetric About x = a
Difficulty: Medium · Topics: Calculus, Integration, Symmetry
x = a ga nisbatan simmetrik funksiya
The continuous function f(x) satisfies
f(a+x)=f(a-x) and ∫ 0^af(x) dx=8.
Evaluate ∫ 0^a\f(2x)+f(2a-x)\ dx. (a is a constant)
Uzluksiz f(x) funksiya quyidagilarni qanoatlantiradi:
f(a+x)=f(a-x) va ∫ 0^af(x) dx=8.
∫ 0^a\f(2x)+f(2a-x)\ dx ni hisoblang. (a — o‘zgarmas)