Applications of Integration Concepts Flashcards
1
Q
What makes p(x) a probability density function?
A
- p(x) >= 0
- integral of p(x)dx for range S = 1
2
Q
P(a ≤ x ≤ b) = ?
A
integral of p(x)dx from a to b
3
Q
mean of p(x) = ?
A
integral of x*p(x)dx for range S = µ
4
Q
Arc length for f(x) = ?
A
S = integral of sqrt(1+(f’(x))^2)dx
for a to b
5
Q
Surface area for f(x) = ?
A
SA = integral of 2πf(x)sqrt(1+(f’(x))^2)dx
for a to b
6
Q
Equation for fluid force = ?
A
F = integral of ρ h(x) w(x) dx for a to b
7
Q
Center of mass for x = ?
A
= integral of x(f(x)-g(x))dx for a to b /
integral of (f(x)-g(x))dx for a to b
8
Q
Center of mass for y = ?
A
= integral of (f^2(x) - g^2(x))/2 dx for a to b /
integral of (f(x)-g(x))dx for a to b
