Calculus I - Area Between Curves (Assignment Problems)

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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 $y = 4$ .