Find the bounded by area the curves -Z+2x and y=13-x2 a) Sketch CuLues rough graph of Goth carves the same axes on proper integral t (No de cinale 6.) Evaluate Tind the area .
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![# Calculating the Area Bounded by Curves
This exercise focuses on finding the area bounded by two linear equations. Follow the instructions below to solve the problem.
**Problem Statement:**
You are given two linear equations:
1. \( y = -2x + 2 \)
2. \( y = 15x - 2 \)
**Tasks:**
a) **Sketch a Rough Graph:**
- Draw both equations on the same set of axes.
- Identify the points of intersection and the area between the curves.
b) **Evaluate the Proper Integral:**
- Calculate the area enclosed by the two curves using integration.
- Ensure your answer is in exact form; use no decimals.
**Instructions:**
1. **Graphing the Equations:**
- Start by rewriting the equations if necessary for easy graphing (i.e., slope-intercept form).
- Find the intersection points by setting the equations equal to each other: \( -2x + 2 = 15x - 2 \).
- Graph the lines based on the slope and y-intercept found in each equation.
2. **Integration:**
- Determine the limits of integration by solving for the points of intersection.
- Subtract one function from the other to find the function to integrate.
- Calculate the definite integral to find the enclosed area.
By completing these steps, we find the area bounded by the curves \( y = -2x + 2 \) and \( y = 15x - 2 \) using both graphical and analytical methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c307513-d57a-4587-a417-fdbdd2c400b3%2Fe00bcf18-724b-4f9f-9de6-cc0a963b6d7b%2Fxgbyi3_processed.jpeg&w=3840&q=75)
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