To calculate the area enclosed by the parabola y2=x+3y and the Y-axis, we can follow these steps: Step 1: Rewrite the equation of the parabolaWe start with the equation of the parabola:y2=x+3yRearranging this gives:y2−3y=x Step 2: Complete the squareTo make it easier to analyze...
Step 2: Find the points of intersectionTo find the area between the curves, we first need to determine the points where the parabola intersects the line x=2. Substituting x=2 into the parabola equation:y2=8(2)=16⟹y=±4Thus, the points of intersection are (2,4) and (2,−4)....
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Given Data: The given parabola is: {eq}y = 4x - {x^2} {/eq} Substitute {eq}y=0 {/eq} in the given parabola equation to find the intersection...Become a member and unlock all Study Answers Start today. Try it now Create an account...
This occurs when the quadratic equation that results from equating the functions has two real solutions. Answer and Explanation: Part 1. Define the area of integration $$\begin{align} y(x) &=x^2-9 && \bigg\{ \textrm {Parabola with center at } \quad (0,9) \quad \text...
Find k so that the area of the finite region bounded by the curve of y=−x(x−k)y=−x(x−k) and the x axis is equal to 4/3 units2. Solution to Example 5. The graph of the given function is a parabola that opens downward and has two x intercepts: x = 0 and x = ...
Parabola upright; roots negative or complex Parabola upright; one positive root v < qw and ev > q v < qw and ev < q Break-even exists Never profitable Parabola inverted; one positive root Parabola inverted; no positive roots These four inequalities determine whether or not a break...
In this case, the upper bound with be the higher values of y, or the parabola. The lower bound would then be the lower values of y, or sloped line. You should have enough information to set up and work out the integral by yourself now. I'll tell you that the final answer is abou...
Step by step video & image solution for Find the area of the region bounded between the parabola x^(2)=y and the curve y=|x|. by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. Updated on:21/07/2023 ...