Do you recall a time in your life when nothing changed? Such times are uncommon, because everything in our lives is vulnerable to change. The amount of food we consume on a daily basis, the number of steps we take, and even the time the Sun rises. Calculus is a mathematical discipline that allows us to explore continuous change. Most people think of calculus as a series of equations with a lot of calculations, but it is actually a set of concepts that we use in our daily lives.

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What exactly is calculus, and what are its several types?

Calculus is a branch of mathematics that studies and analyses rates of change and looks for patterns between equations. It is an important area in mathematics. Nevertheless, before delving into calculus, you must first learn the meaning of three terms: function, derivative, and integral.

A function in an equation specifies the relationship between two variables (such as distance and time, temperature and volume, and so on). A function is made up of three parts: an input or set of inputs, an output or set of outputs, and a rule that assigns each input to exactly one output.

The derivative is defined as a function's rate of change with respect to a variable (i.e. output value with respect to input value). A mathematical object known as an integral can be regarded as an area or a generalisation of area.

What exactly is differential calculus?

Differential calculus is the branch of calculus that seeks to determine the rate of change of a function with regard to the variable on which it relies. It is frequently used to calculate the slope of a line (how steep it is) at a particular point on a curve.

While determining the slope of a straight line is relatively simple, the slope of a curve varies at different locations as the line bends. One method for determining the slope is to mathematically split the curve into extremely small pieces, each of which resembles a straight line. This straight line's slope will therefore be the same as the slope of the curve at that point, which is known as the tangent.

What exactly is integral calculus?

Whereas differential calculus is largely concerned with the slope of a curve. Integral calculus, on the other hand, is concerned with computing the area beneath a function graph.

For example, if we want to calculate the distance travelled by a car and know its speed at various periods in time, we may construct a graph of that speed and the distance travelled will be the area under the graph.

This is accomplished by breaking the graph into several extremely small parts and "drawing" rectangles beneath each component. Because the area of a rectangle is simple to compute, the total area of all rectangles may be determined. If the rectangles are narrow enough, the total area will be close to the area beneath the graph. The integral of the function is the value of the area.