Integral calculus calculates the area under a curve of a mathematical function, with wide applications in physics and engineering. Isaac Newton and Gottfried Leibniz were pioneers of calculus, but Newton’s accusations of plagiarism destroyed Leibniz’s reputation. Integration works by summing an infinite number of infinitesimal strips to give the exact value of the area. Calculus is used to describe how a function changes with respect to time.
Integral calculus, also known as integration, is one of the two branches of calculus, the other being differentiation. Differentiation describes how the value of a function changes with respect to its variables. Integration is the reverse, as it gives the exact sum of a function between two values. Integral calculus provides an exact means of calculating the area under the curve of a mathematical function. Integration has a wide range of applications in physics and engineering.
The two pioneers of calculus were the 17th century scientists Isaac Newton and Gottfried Leibniz. The mathematical notation used today is based on the work of Leibniz. While undoubtedly a great scientist, Newton had a reputation for being highly competitive and vindictive, and he was unwilling to share credit with his German contemporary. Newton used his considerable influence at the Royal Society of London to directly and indirectly accuse Leibniz of plagiarism. The validity of these allegations has never been tested, but the controversy has destroyed Leibniz’s reputation.
Integration is best described in terms of the area under the curve of a mathematical function. This area can be thought of as the sum of vertical stripes of equal width. A few wide strips will give an approximate value for the area; increasing the number of strips and decreasing their width will give an increasingly accurate value for this area. The integral calculus works by considering when the width of these strips tends to 0, and therefore the number of strips tends to infinity. The summation of an infinite number of infinitesimal strips gives the exact value of the area.
Calculus is used to describe how a function (f) changes with respect to time
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