All tools › Calculus
Area under a curve
Four rules compared, with the strips drawn
It runs entirely in this browser tab: what you type is never uploaded, and the arithmetic is exact — nothing here was ever a floating-point number.
Settings
- Variable
- Which letter to work with, when there is more than one
- From
- Where the range starts
- To
- Where the range ends
- Strips
- How many pieces the range is cut into A number from 2 to 1000.
- Decimal places
- How far an approximate answer is taken A number from 0 to 12.
- Compare the rules
- All four side by side on the same number of strips
- Draw it
- A picture of the answer as well as the numbers
How to use it
- Paste your text into the box above, or open a file.
- Adjust the settings beside it until the result is what you wanted.
- Copy the result, or save it as a file. The result updates as you type.
Questions
- Is what I type uploaded anywhere?
- No. The whole application is carried as WebAssembly and runs on your own device. There is no server to send anything to, and none of these tools makes a network request while it works.
- Why does it matter that there is no floating point?
- Because these tools show their working. In floating point an elimination produces rows with 0.0000000000000002 where a zero belongs, and every step after it is decided by a tolerance somebody picked. In fractions the zero is a zero: the rank is a count, a determinant of a matrix of thirds is a third, and a matrix times its inverse is exactly the identity.
- Can I use it in an exam or for homework?
- That is between you and whoever set the work. What these give you is the method as well as the answer, which is usually what is being marked: the rule at each step, the substitution written out, the intermediate matrices, the table of values.
- Why does a tool sometimes refuse instead of answering?
- Because the honest answer is sometimes that there is none. An integral with no elementary antiderivative, a matrix with no inverse, a bisection over an interval with no sign change, a logarithm of zero: each is a fact rather than a failure, and a plausible number in its place would be worse than the refusal.
Other tools for calculus
Derivative
Symbolic, with the rule named at every step
Integral
The forms it recognises, and plain honesty about the rest
Limit
From each side, with the table of approach that is the evidence
Roots of a function
Bisection, Newton and secant, with every iteration shown
All twenty-eight tools