7.5 Area Between Curvesap Calculus

.ﬁnd the area between a curve and the x-axis, where the ordinates are given by the points where the curve crosses the axis;.ﬁnd the area between two curves. Introduction 2 2. The area between a curve and the x-axis 2 3. Some examples 4 4. The area between two curves 7 5. Another way of ﬁnding the area between two curves 9. Think about it: the area between the two curves is equal to the area under the top function minus the area that is under the bottom function. The people who don't like words can start paying attention again. We have two brand-spanking new formulas. Aren't you just itching to try them? An area of zero doesn't quite make sense here, so using the straight integral is insufficient. What we can do is treat this as two separate integrals, one where the area is above the x-axis and one where it is below and add their effective area. Sinx = 0, x = 0, π, 2π in this interval. A = ∫ 0 π sinx dx + (−∫ π 2π sinx dx). 8.4 Area Between Curves (with respect to x) 8.5 Area Between Curves (with respect to y) 8.6 Area Between Curves - More than Two Intersections Mid-Unit Review - Unit 8 8.7 Cross Sections: Squares and Rectangles 8.8 Cross Sections: Triangles and Semicircles 8.9 Disc Method: Revolving Around the x- or y- Axis 8.10 Disc Method: Revolving Around. Figure 7.5 g, 0,x 1 f, NOTE The height of a representative rectangle is regardless of the relative position of the axis, as shown in Figure 7.4. X-f x g x Area of a Region Between Two Curves If and are continuous on and for all in then the area of the region bounded by the graphs of and and the vertical lines and is A b a f x g x dx.

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7.5 Area Between Curves Ap Calculus Formulas

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Section 6-2 : Area Between Curves

1. Determine the area below (fleft( x right) = 3 + 2x - {x^2}) and above the x-axis. Solution
2. Determine the area to the left of (gleft( 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.

1. (y = {x^2} + 2), (y = sin left( x right)), (x = - 1) and (x = 2) Solution
2. (displaystyle y = frac{8}{x}), (y = 2x) and (x = 4) Solution
3. (x = 3 + {y^2}), (x = 2 - {y^2}), (y = 1) and (y = - 2) Solution
4. (x = {y^2} - y - 6) and (x = 2y + 4) Solution
5. (y = xsqrt {{x^2} + 1} ), (y = {{bf{e}}^{ - ,frac{1}{2}x}}), (x = - 3) and the y-axis. Solution
6. (y = 4x + 3), (y = 6 - x - 2{x^2}), (x = - 4) and (x = 2) Solution
7. (displaystyle y = frac{1}{{x + 2}}), (y = {left( {x + 2} right)^2}), (displaystyle x = - frac{3}{2}), (x = 1) Solution
8. (x = {y^2} + 1), (x = 5), (y = - 3) and (y = 3) Solution
9. (x = {{bf{e}}^{1 + 2y}}), (x = {{bf{e}}^{1 - y}}), (y = - 2) and (y = 1) Solution