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Section 6.2 : Area Between Curves
- Determine the area below \(f\left( x \right) = 3 + 2x - {x^2}\) and above the x-axis. Solution
- Determine the area to the left of \(g\left( y \right) = 3 - {y^2}\) and to the right of \(x = - 1\). Solution
For problems 3 – 11 determine the area of the region bounded by the given set of curves.
- \(y = {x^2} + 2\), \(y = \sin \left( x \right)\), \(x = - 1\) and \(x = 2\) Solution
- \(\displaystyle y = \frac{8}{x}\), \(y = 2x\) and \(x = 4\) Solution
- \(x = 3 + {y^2}\), \(x = 2 - {y^2}\), \(y = 1\) and \(y = - 2\) Solution
- \(x = {y^2} - y - 6\) and \(x = 2y + 4\) Solution
- \(y = x\sqrt {{x^2} + 1} \), \(y = {{\bf{e}}^{ - \,\,\frac{1}{2}x}}\), \(x = - 3\) and the y-axis. Solution
- \(y = 4x + 3\), \(y = 6 - x - 2{x^2}\), \(x = - 4\) and \(x = 2\) Solution
- \(\displaystyle y = \frac{1}{{x + 2}}\), \(y = {\left( {x + 2} \right)^2}\), \(\displaystyle x = - \frac{3}{2}\), \(x = 1\) Solution
- \(x = {y^2} + 1\), \(x = 5\), \(y = - 3\) and \(y = 3\) Solution
- \(x = {{\bf{e}}^{1 + 2y}}\), \(x = {{\bf{e}}^{1 - y}}\), \(y = - 2\) and \(y = 1\) Solution