Matematik A-niveau Termer

Integrationsgrænser

Integration limits define the interval over which the definite integral is calculated. They specify the starting and ending points of the integration.

Riemann Sum

A Riemann sum is an approximation method used to estimate definite integrals by dividing the interval into smaller subintervals and using rectangles (rektangler) to approximate (estimere) the area.

Deler

A bisector is a line or line segment that divides an angle or line segment into two equal parts.

Bestemt Integral

A definite integral represents the net accumulation (nettoakkumulering) of a quantity over a specific interval (over et specifikt interval) or range. It provides a numerical value and is often used to find areas under curves.

Grænseværdi

A limit is a fundamental concept in differentiation and integration, used to describe the behavior of a function as a value approaches a certain limit(bestemt grænse).

Linje

A line

Normalvektor

A normal vector to a surface (en flade) or curve is a vector that is perpendicular (vinkelret) to the surface or curve at a given point and is used in various contexts (sammenhænge) within vector functions.

Punkt

A point

Retningsvektor

A unit vector is a vector with a magnitude of 1 that represents the direction of another vector. It is essential for describing the direction of motion (bevægelsesretning). Det er en enheds vektor.

Vektor funktioner

A vector function is a function that assigns a vector to each value of an independent variable, often represented as r⃗(t), where r⃗ is the vector, and t is the independent variable(uafhængig variable), typically time.

Parallele linjer

Parallel lines are two or more lines that are equidistant and never intersect. They have the same slope.

Parameterisering

Parameterization is the process of describing a curve using a parameter (usually time). It involves expressing the position of the curve as a function of this parameter.

Delbrøksopdeling

Partial fraction decomposition is a technique used to simplify rational functions by breaking them down into simpler (enklere) fractions (brøker).

Omkreds

Perimeter

Lodrette linjer/Ortogonale

Perpendicular lines are two lines that intersect at a 90-degree angle, forming right angles.

Polygoner

Polygons

Stråle

Ray

Retvinklet trekant

Right triangle. The side opposite the right angle is called the hypotenuse.

Similaritet

Similarity refers to the relationship between two shapes that have the same shape but possibly different sizes. Similar shapes have corresponding angles that are congruent.

Farten

Speed is the magnitude of the velocity vector, representing the object's overall speed regardless of direction.

Firkant

Square

Integrationssymbol(∫)

he integration symbol (∫) is used to indicate that a function is being integrated. It precedes the function to be integrated.

Antiderivativ

An antiderivative is a function whose derivative is equal to the given function. It is found through indefinite integration (ubestemt integration).

Ubestemt Integral

An improper integral is an integral with one or both limits extending to infinity or where the integrand has an infinite discontinuity.

Ubestemte Integral

An indefinite integral, also known as an antiderivative, represents a family of functions whose derivative is the given function (hvis afledede er den givne funktion). It includes an arbitrary (vilkårlig) constant of integration (C).

Integral

An integral is a mathematical concept used to find the accumulated quantity (akkumulerede mængde) or total of a quantity (total mængde) that changes continuously. It is represented by the symbol ∫ and is used to calculate areas, volumes, and other quantities.

Vinkel

Angle

Areal

Area

Cirkel

Circle

Onkreds

Circumference Formula C=2πr

Kongurens

Congruence refers to the relationship between two shapes that have the same shape and the same size. Congruent shapes have both equal angles and equal side lengths.

Areal under en kurve

Integrals are often used to calculate the area (beregne arealet) under a curve in a two-dimensional graph (to-dimensionelt diagram/graf). The definite integral provides the area between the curve and the x-axis over a specified interval.

Integral

Integrals are used to calculate (beregne) the accumulated result of a function over an interval and play a central role in finding, for example, distance (afstand) and the area (areal/område) under a curve.

Areal mellem Kurver

Integrals can be used to find the area between two curves in a two-dimensional graph. The absolute difference (Forskellen) between the two functions represents the area.

Volumen af Revolution

Integrals can be used to find the volume of a three-dimensional shape created by rotating a curve or region about an axis, such as a solid of revolution (en roteret figur)

Linjestykke

Line segment

Fundamental Sætning om Integralregning

The Fundamental Theorem of Calculus establishes a fundamental link between differentiation and integration. It states that the definite integral of a function can be found by evaluating its antiderivative at the endpoints of the interval. Den siger, at det bestemte integral af en funktion kan findes ved at evaluere dens antiderivativ ved intervallets endepunkter.

Pythagoras Sætning

The Pythagorean Theorem is a fundamental relationship for right triangles. It states that the square of the hypotenuse's length is equal to the sum of the squares of the other two sides' lengths: c2=a2+b2.

Akselerationsvektor

The acceleration vector represents the change (ændringen) in velocity(hastighed) with respect to time and is usually derived from the velocity vector. It is denoted as a⃗(t).

Integrationsvariabel

The integration variable is the variable with respect to which the integration is performed. It appears in the integrand and represents the quantity being accumulated.

Substitutionmetoden

The substitution method is used to simplify an integral by introducing a new variable. It makes certain integrals easier to evaluate.

Tangentlinje

The tangent line to a curve at a specific time is a straight line (ret linje) that touches the curve exactly at that time (tidspunkt) and has the same slope (hældning) as the curve at that point.

Hastigheds vektor

The velocity vector represents the object's instantaneous velocity (øjeblikkelige hastighed) and is usually the derivative (afledt) of the vector function (r⃗(t)) with respect to time. It is denoted as v⃗(t).

Trekant

Triangle

Trigonomiske Identiteter

Trigonometric identities are used to simplify integrals involving trigonometric (trigonomiske) functions. Common identities include sine (sinus), cosine (cosinus), and tangent identities.

Komponenter

Vector functions typically consist of components that describe the object's position in different directions (retninger). These can be expressed as ex. x(t) and y(t)

Kurver og baner:

When working with vector functions, "curves" (Kurver)and "paths" (Baner) are often the geometric shapes (geometriske former) that describe how objects move in space (rummet)