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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- For what values of \(x\) satisfying \(a < x < e\) is the function \(y = f(x)\) not differentiable?
- What is the value of the definite integral of \(f(x)\) from \(x = a\) to \(x = 0\)? Explain your answer.
- What is the value of the definite integral of \(f(x)\) from \(x = b\) to \(x = c\)? Explain your answer.
- 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 \(x = e\)?
- What is the value of the definite integral of \(f(x)\) from \(x = -2\) to \(x = 10\)?
- What is total area bounded by \(y = f(x)\), the \(x\)-axis and the ordinates \(x = a\) and \(x = e\)?