First, we need to find out where the curve meets the x-axis (y=0), so it’s clear that x=0 and x=3 are the limits.
We can write the area as an integral: ∫ydx[0,3] where the limits are in square brackets.
Substitute for y: ∫(3x⁵-x⁶)dx=(x⁶/2-x⁷/7)[0,3]=3⁶(1/2-3/7)=729/14=52¹⁄₁₄ or 52.07͒14285͒ where ͒ indicate a recurring decimal.
The curve in red is a thin sliver between x=0 and x=3 as shown. The required area is clearly seen.