Evaluate ∫₀³ x² dx

The value of lim(x→0) (sin x)/x is:

If ∫₀^1 (x⁴(1-x)⁴)/(1+x²) dx = 22/7 - π, find the value of 7∫₀^1 (x⁴(1-x)⁴)/(1+x²) dx + 7π rounded to nearest integer.

The area enclosed between the curves y = x² and y = x is:

The value of the integral ∫₀^π x·sin²(x)·cos(x) dx is: