Accumulate quantities such as area, displacement and charge; the reverse of differentiation.
The integral accumulates a quantity: ∫f dx is the area under f. The indefinite integral gives antiderivatives plus constant C, definite integrals give numbers. Integration finds distance from velocity, charge from current and work from force.
∫₀³ 2t dt = 9 m if v=2t m/s.
Integrals accumulate quantities over time or space, so they give charge from current, displacement from velocity and mass from density.
Accumulate quantities such as area, displacement and charge; the reverse of differentiation.
Integrals accumulate quantities over time or space, so they give charge from current, displacement from velocity and mass from density.
An indefinite integral is a family of antiderivatives with a constant. A definite integral has limits and gives a single number, the net accumulated quantity.
Any two antiderivatives differ by a constant, so the constant records the initial condition that the problem supplies.
Typical applications include computing the charge that flows through a resistor from a current profile, finding the total energy from a power curve and calculating the area of a cross-section for a volume estimate.
Study "Maxima and minima" first (topic 31 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Integral of xⁿ = xⁿ⁺¹/(n+1)+C. Linear in sums and constants. Area below the axis counts negative.
∫₀³ 2t dt = 9 m if v=2t m/s.
The next topic is "Fundamental theorem of calculus", which builds directly on this one.
It is classed as Beginner in Engineering Mathematics (topic 32 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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