Integration & Antiderivatives (College Board AP® Calculus AB)

Work out the indefinite integral .

The rate of change of a curve is given by . Given that the curve passes through the point , find the equation of the curve in terms of .

The function is used to model the surface area of a pond, in square meters, that is covered by a particular species of invasive pond weed. The rate of change function for is , with the rate of change at time given by . Given that 1 square meter of the pond is covered by the weed at at time , find an expression for .

A function satisfies the equation , where is the derivative of . Given that , find an expression for in terms of .