g is real function continue let
f(x)=∫_0 ^x sin(x−t)g(t)dt
1)prove that f^′ (x)= ∫_0 ^x cos(t−x)g(t)dt
2)prove that f is so<ution of the diff.equa.
y^(′′) +y =g(x)
let give the function f(x)=∫_0 ^π ln(1+xcosθ)dθ with ∣x∣<1
1) find a simple form of f(x)
2)calculate ∫_0 ^π ln(1−cosθ)dθ
3)calculate ∫_0 ^π ln(1+cosθ)dθ.