The area shut in by two curves is the integral of the top one minus the bottom one, taken between the points where they cross. Finding those crossings is the first half of the job.
Find the area of the region enclosed by y=6−x2 and y=2
They cross where 6 minus x squared equals 2, so at x equals 2 and x equals negative 2.
Between those the parabola is on top, so integrate 4 minus x squared from negative 2 to 2.
That comes to 32 over 3.
The answer is 332.
Where students go wrong
Integrating the difference straight through when the curves cross in the middle. Past a crossing the other one is on top, so that stretch subtracts from the answer instead of adding to it. Split at every crossing and take each piece positive.
Also called area between curves, area enclosed by two curves, region between two graphs or definite integral of a difference.
Questions about these worksheets
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Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
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That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the area between two curves questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Integrating the difference straight through when the curves cross in the middle. Past a crossing the other one is on top, so that stretch subtracts from the answer instead of adding to it. Split at every crossing and take each piece positive.