An Average Over a Vanishing Interval

Difficulty: Hard · Topics: Calculus, Integration, Limits

Yo‘qolib boruvchi oraliq bo‘yicha o‘rtacha

For the function

f(x)=∫ -(π)/(2)^x1/2sin 2t (sin t+1) dt,

find the value of

lim h→ 01/h∫ (π)/(2)-h^(π)/(2)+hf(t) dt.