Apostol Calulus Voume1 I 2.4 question 9

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SUMMARY

The discussion focuses on calculating the area of the region S between the graphs of the functions F(x) = x² and g(x) = x + 1 over the interval [-1, (1 + √5)/2]. Participants express concerns about the complexity of finding the intersection points of the two functions, which is essential for accurately determining the area. The problem emphasizes the necessity of sketching the graphs to visualize the shaded area representing S. Clear identification of intersection points is crucial for solving the problem correctly.

PREREQUISITES
  • Understanding of calculus concepts, specifically integration.
  • Familiarity with graphing quadratic functions and linear functions.
  • Knowledge of solving equations to find intersection points.
  • Ability to compute definite integrals to find areas between curves.
NEXT STEPS
  • Study the method for finding intersection points of functions.
  • Learn how to compute definite integrals for area calculation between curves.
  • Practice sketching graphs of quadratic and linear functions for better visualization.
  • Explore the application of the Fundamental Theorem of Calculus in area problems.
USEFUL FOR

Students studying calculus, particularly those focusing on area calculations between curves, as well as educators seeking to enhance their teaching methods in this topic.

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1. Compute the area of the region S between the graphs of f and g over the interal [a,b] specified in each case Make a sketch of the two graphs and indicate S by shading.

Question 9 -F(x)=x^2 g(x)=x+1,a =-1, b = (1+√5)/2




Homework Equations





The Attempt at a Solution


I think Ihave the solution,it's just that the intersection points are a bit messy. Is it supposed to be this way or am I missing something?
 
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Physics2341313 said:
1. Compute the area of the region S between the graphs of f and g over the interal [a,b] specified in each case Make a sketch of the two graphs and indicate S by shading.

Question 9 -F(x)=x^2 g(x)=x+1,a =-1, b = (1+√5)/2




Homework Equations





The Attempt at a Solution


I think Ihave the solution,it's just that the intersection points are a bit messy. Is it supposed to be this way or am I missing something?

What do you mean when you say "...the intersection points are a bit messy"? Messy how? Anyway, since we cannot see what you did, how are we supposed to answer?
 

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