We at times are interested in determining the area between two curves defined on an interval. This is depicted below. This sort of situation arises when one wants to find differences between totals of quantities that continuously vary.
Thankfully, finding the area between two curves is easy!
If you look at the second formula above, the first integral gives you the area under the top function
Note that the first formula is nothing more than a combination of the two integrals into a single integral using the additive property for antiderivatives/integrals.
More often than not, we are not given the graphs of the two functions whose graphs we want to find the area between. As such, in order to use the formula above, we need to determine which function is the “top” function. This is easy, assuming that your functions don’t cross: Simply take your favorite
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area
Subtract the lower function from the higher, then integrate the result.
Area between
Computing areas between two curves on an interval:
Area