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Practice Problems for 4/17

  1. Let \(f(x)=2+\sin x\). Suppose we approximate the area under \(f(x)\) on \([0,2\pi]\) using right endpoints of the subintervals. On which intervals would the corresponding rectangles give an over-approximation and on which intervals would the area of the rectangles give an under-approximation?

  2. Let \(v(t)\) be the velocity of a projectile. What does the area under the function \(v(t)\) correspond to, and what does the area under \(|v(t)|\) correspond to?

  3. Find an expression approximating the area of a circle of radius \(r\) using an \(n\) sided polygon, with sides of equal length.