Home > Calculus > Calculating Areas using Integrals

How do you find the area between #f(x)=x^2-4x+3# and #g(x)=-x^2+2x+3#?

Answer 1

Emilia Aguilar

See answer below:

Continuation:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isabella Ackerman

To find the area between ( f(x) = x^2 - 4x + 3 ) and ( g(x) = -x^2 + 2x + 3 ), you first need to find the points where the two functions intersect. Set ( f(x) ) equal to ( g(x) ) and solve for ( x ). Then integrate the absolute difference between the two functions over the interval where they intersect. The area can be calculated as the integral of the absolute difference between the two functions over the interval of intersection:

[ A = \int_{a}^{b} |f(x) - g(x)| , dx ]

where ( a ) and ( b ) are the ( x )-values of the points of intersection.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.