Calc I in class problems
on beginning integration
Use the fundamental theorem of calculus to evaluate \[ \int_0^2 (4x^3 - x + e^x)\,dx. \]
Suppose an object starts at \(x(0)=1\) and has velocity given by \(x'(t) = 2t - 1\). Find the position of the object at time \(t=2\).
The complete graph of a function \(f\) is shown in the figure below; it consists of a quarter circle and a straight line segment. Evaluate \[ \int_{-2}^3 f(x) \, dx. \]