The formula for the integration is: {eq}\displaystyle \int x^ndx = \dfrac{x^{n+1}}{n+1} {/eq} The area is given by: {eq}Area = \displaystyle \int_{x_2(lower\ limit)}^{x_1(upper\ limit)} (upper\ curve - lower\ curve)dx {/eq} ...
To find the area bounded by the curves we will use the formula: {eq}\int (f(x)-g(x))dx {/eq} Here f(x) is the curve that lies above g(x) Now let...Become a member and unlock all Study Answers Try it risk-free for 30 days Try it risk-free Ask a ...
Calculation of Work Using Integration(applications of integration)Work done by some force is usually calculated by formulaW=F.dhere we assume that the force is constant. But If we look at our day to day examples no force is constant. Force is different at every point. If a force any poin...
Find the area bounded by the curves y = (x^2) + 4 and y = x + 2. Find the area bounded by the curves: y=(x-1)^3, y=(x-1). Find the area bounded by the curves y = x^2 - 2x + 5 and y = 3x - 1. Find the area bounded by the curves y = ...
Ify=f(x)is a curve then,area under curves bounded by limits[a,b]is given byA=∫abf(x)dx. Area between two curves is given by difference of area under individual curves. Formula Used: ∫xndx=xn+1n+1+c. Answer and Explanation:1 ...
Find the area of the region bounded by the curvey=x2and the liney=4. View Solution Find the area of the region bounded by the curve(y−1)2=4(x+1)and the line y= x-1 View Solution Find the area of the region bounded by the curvey=x2and the liney=4. ...
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This will give you the total area enclosed by the three curves. What is the formula for finding the area between 3 curves?The formula for finding the area between 3 curves is: A = ∫(f(x) - g(x)) dx, where f(x) represents the upper curve, g(x) represents the lower curve, ...
also included.Examples with Detailed SolutionsExample 1Find the area of the region bounded by y = 2x, y = 0, x = 0 and x = 2.(see figure below).Figure 2. Area under a curve example 1.Solution to Example 1Two methods are used to find the area.Method 1This problem may be solved...
The curve y = f(x), completely above the x-axis. Shows a "typical" rectangle, Δx wide and y high.In this case, we find the area by simply finding the integral:Area=∫abf(x)dxArea=∫abf(x)dxWhere did this formula come from?Area...