Question

How do I find the derivative of

⌠lnx
⌡π cos(e^(t))dt


The question above is asking for the derivative of the integral cos(e^(t))
from pi to lnx

Answer 1

since

d/dx ∫[a(x),b(x)] f(t) dt = f(b(x))db/dx - f(a(x))da/dx, we have

cos(e^(lnx)) d/dx(ln(x)) - cos(e^π) d/dx(π)
= cos(x) * 1/x - 0
= cos(x)/x

check the examples on wikipedia for differentiation under intagral.

Answer 2

okay thank you!