Which among the following correctly defines Leibnitz rule of a function given by \( f (α) = \int_a^b (x,α)dx\) where a
Posted: Thu Jul 14, 2022 9:29 am
a) \(f’(α) = \int_a^b \frac{∂}{∂α} f(x,α) dx\)
b) \(f’(α) = \frac{d}{dα} \int_a^b f(x,α) dx\)
c) \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx + f(b, α) \frac{da}{dα} – f(a, α) \frac{db}{dα}\)
d) \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx + f(b, α) \frac{db}{dα} – f(a, α) \frac{da}{dα}\)
b) \(f’(α) = \frac{d}{dα} \int_a^b f(x,α) dx\)
c) \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx + f(b, α) \frac{da}{dα} – f(a, α) \frac{db}{dα}\)
d) \(f’(α) = \int_a^b \frac{∂}{∂α} f (x,α) dx + f(b, α) \frac{db}{dα} – f(a, α) \frac{da}{dα}\)