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Assignment Problems Notice
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 6.2 : Area Between Curves
- Determine the area below \(f\left( x \right) = 8x - 2{x^2}\) and above the x-axis.
- Determine the area above \(f\left( x \right) = 3{x^2} + 6x - 9\) and below the x-axis.
- Determine the area to the right of \(g\left( y \right) = {y^2} + 4y - 5\) and to the left of the y-axis.
- Determine the area to the left of \(g\left( y \right) = - 4{y^2} + 24y - 20\) and to the right of the y-axis.
- Determine the area below \(f\left( x \right) = 10 - 2{x^2}\) and above the line \(y = 3\).
- Determine the area above \(f\left( x \right) = {x^2} + 2x + 3\) and below the line \(y = 11\).
- Determine the area to the right of \(g\left( y \right) = {y^2} + 2y - 4\) and to the left of the line \(x = - 1\).
- Determine the area to the left of \(g\left( y \right) = 2 + 4y - {y^2}\) and to the right of the line \(x = - 1\).
For problems 9 – 26 determine the area of the region bounded by the given set of curves.
- \(y = {x^3} + 2\), \(y = 1\) and \(x = 2\).
- \(y = {x^2} - 6x + 10\) and \(y = 5\).
- \(y = {x^2} - 6x + 10\), \(x = 1\), \(x = 5\) and the x-axis.
- \(x = {y^2} + 2y + 4\) and \(x = 4\).
- \(y = 5 - \sqrt x \), \(x = 1\), \(x = 4\) and the x-axis.
- \(x = {{\bf{e}}^y}\), \(x = 1\), \(y = 1\) and \(y = 2\).
- \(x = 4y - {y^2}\) and the y-axis.
- \(y = {x^2} + 2x + 4\), \(y = 3x + 6\), \(x = - 3\) and \(x = 3\).
- \(x = 6y - {y^2}\), \(x = 2y\), \(y = - 2\) and \(y = 5\).
- \(y = {x^2} + 8\), \(y = 3{x^2}\), \(x = - 3\) and \(x = 4\).
- \(x = {y^2}\), \(x = {y^3}\) and \(y = 2\).
- \(\displaystyle y = \frac{7}{x}\), \(\displaystyle y = \frac{1}{x} - 3\), \(x = - 1\)and \(x = - 4\).
- \(y = 2{x^2} + 1\), \(y = 7 - x\), \(x = 4\) and the y-axis.
- \(\displaystyle y = \sin \left( {\frac{1}{2}x} \right)\), \(y = 3 + \cos \left( {2x} \right)\), \(x = 0\) and \(x = \frac{\pi }{4}\).
- \(x = \sqrt {2y + 6} \), \(x = y - 1\), \(y = 1\) and \(y = 6\).
- \(y = 2 - {{\bf{e}}^{2 - x}}\), \(y = {x^2} - 4x + 7\), \(x = 3\) and the y-axis. Note : These functions do not intersect.
- \(y = {{\bf{e}}^{2x - 1}}\), \(y = {{\bf{e}}^{5 - x}}\), \(x = 0\) and \(x = 3\).
- \(x = \cos \left( {\pi y} \right)\), \(x = 3\), \(y = 0\) and \(y = 4\).