integrals
Calculus area computations
Integrals are fundamental operations in calculus that determine the accumulation of quantities—areas under curves, total distances, or sums of infinitely small parts.
Where derivatives measure rates of change, integrals reverse that process, finding the whole from its pieces.
Solving integrals took up most of the exam.
The integral sign ∫ represents this operation, with definite integrals yielding specific values and indefinite integrals yielding functions.
Function's rate of change
- antiderivativeReverse of differentiation
- differentiationRecognizing meaningful differences
- limitMaximum allowed extent
- areaExtent of surface
volume · curve · function · u-substitution · definite · indefinite · chain rule · product rule
Edges or leaps
- limitsImposed maximum points
- summationAdding to find total
- sigmaEighteenth Greek letter
- LeibnizBaroque-era polymath philosopher-mathematician
Newton · integrand · differential · evaluate · notation
Extent of surface
- volumeAmount of space filled
- displacementRemoval from usual location
- workEffort toward a goal
- probabilityQuantified chance of occurrence
expected value · center of mass · moment · accumulation · flow · circulation · density · physics
Process of approaching sameness
- divergenceSeparation from common origin
- continuityUninterrupted progression or coherence
- measureUnit of quantity
- contourBounding line of shape
derivative
Function's rate of change
- antiderivativeReverse of differentiation
- differentiationRecognizing meaningful differences
- limitMaximum allowed extent
area · volume · curve · function · u-substitution · definite · indefinite · chain rule · product rule · bounds
bounds
Edges or leaps
Leibniz · Newton · integrand · differential · evaluate · notation
area
Extent of surface
- volumeAmount of space filled
- displacementRemoval from usual location
- workEffort toward a goal
probability · expected value · center of mass · moment · accumulation · flow · circulation · density · physics · engineering
convergence
Process of approaching sameness
- divergenceSeparation from common origin
- continuityUninterrupted progression or coherence
- measureUnit of quantity
- mathaddition, subtraction, multiplication, division, algebra
- mathematicsalgebra, arithmetic, calculus, geometry, number
- math conceptsangle, numbers, algebra, circle, equations
- Engineering Mathcalculus, algebra, linear algebra, differential equations, matrices
- notationsmusical notation, mathematical notation, decimal notation, scientific notation, dance notation
- calculusderivatives, limits, differential calculus, chain rule, differentiation
integralsderivatives
Things derived from another
differentials · differentiation · differential calculus · slopes · gradients
integralspartials
Incomplete sets or components
fragments · increments · differentials · infinitesimals · fractions
- ethnic integrationCombining distinct cultural groups
- integral calculusMathematics of antiderivatives
- integrated schoolsRacially mixed educational institutions
- integral part
- integrated circuitsMiniaturized electronic components on semiconductor
- racial integrationUnifying separated ethnic groups
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