Dynamic Calculus

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Areas of regions (Part 1)

The graph of the function y = f(x) consists of straight line segments and two quarter circles as shown below. The shape of the function can be altered by moving the blue points at x = a, b, c and d.
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  1. For what values of \(x\) satisfying \(a < x < e\) is the function \(y = f(x)\) not differentiable?
  2. What is the value of the definite integral of \(f(x)\) from \(x = a\) to \(x = 0\)? Explain your answer.
  3. What is the value of the definite integral of \(f(x)\) from \(x = b\) to \(x = c\)? Explain your answer.
  4. Move the points \(b\) and \(d\) so that Area II is equal Area V. What relationship exists between the value of the definite integral of \(f(x)\) from \(x = 0\) to \(x = b\) and the value of the definite integral of \(f(x)\) from \(x = d\) to \(x = e\)?
  5. What is the value of the definite integral of \(f(x)\) from \(x = -2\) to \(x = 10\)?
  6. What is total area bounded by \(y = f(x)\), the \(x\)-axis and the ordinates \(x = a\) and \(x = e\)?