Find the area of the region enclosed between f(x) = x+5, g(x)= -x+5 and h(x) = -1. (Hint: Draw a Picture).

 

I've drawn the picture but still don't know how to set up the integral.
in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The line h(x)=-1 intersects f(x)=x+5, when -1=x+5, that is, x=-6; and intersects g(x)=-x+5, when -1=-x+5, that is, x=6. f(x)=g(x) gives the intersection of the two functions: x+5=-x+5, 2x=0, x=0. Intersection at (0,5), the common y intercept.

The beauty about this problem is that we don’t need to use integrals to find the required area since it is simply the area of the red isosceles right triangle shown above. The height is 5-(-1)=6 and the base is 6-(-6)=12. Therefore the area is ½(6×12)=36 square units.

(If you’re wondering why you can’t or don’t get the right answer using integrals it’s probably because you didn’t realise that areas below the axis are negative. You can still work it out using integrals but you need the inverse functions for f and g, that is, x in terms of y where y=f(x) or g(x), then you use ∫xdy rather than ∫ydx. If you carefully analyse the integration process for finding areas you will see why areas below the axis are negative.)

by Top Rated User (616k points)

Related questions

1 answer
1 answer
1 answer
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,263 questions
86,786 answers
1,945 comments
3,649 users