Calculus is a branch of mathematics that focuses on the study of rates of change. It is an essential part of many areas, such as physics, engineering, and economics. There are two branches of calculus: differential calculus and integral calculus. Both forms are important, but they are used in different ways and have different applications.
You might wonder if differential calculus is easier than integral calculus. Generally, most of my students find differential calculus relatively easy. Differential calculus focuses on calculating rates of change, while integral calculus deals with finding areas under curves or volumes between two curves. Both forms are extremely useful tools for solving problems in many different scientific fields, from physics and chemistry to engineering and economics.
Read on to find out the key differences between differential calculus and integral calculus. If you are looking to learn calculus, I wrote a whole article about the 9 Best YouTube Channels to Learn Calculus.
What Is Differential Calculus?
Differential calculus is the study of rates of change, or derivatives, in functions, meaning that you can use differential calculus to find out how quickly a function is changing over time (e.g., how fast a car is accelerating).
Typically, differentiation is used to calculate velocity, acceleration, and other rates of change, as well as to find maximums and minimums in a given system. You can also use differentiation to solve equations involving derivatives (the rate at which one quantity changes with respect to another)
In addition, differential calculus allows you to calculate slopes or tangents on curves, which can be useful for finding optimal solutions to many different problems.
What Is Integral Calculus?
Integral calculus is the study of areas under a curve or between two curves, allowing you to solve problems related to area or volume by breaking down shapes into smaller pieces and then summing them up again.
For example, if you wanted to find the volume of an object like a cylinder or cone, you could use integral calculus to break it down into multiple slices and then add those slices together to get the total volume.
Think of integral calculus as the opposite of differential calculus; it focuses on finding the total value of a function by adding up all its parts.
You can use integration to calculate the area under curves, volumes in three-dimensional space, lengths of arcs, and more. It can also be used in solving equations involving integrals (the sum of infinitely many small pieces).
If you are interested I encourage you to watch a video from Khan Academy to learn more about integral calculus.
Should You Learn Differential or Integral Calculus First?
It is generally recommended to learn differential calculus first before considering integral calculus because knowing derivatives is essential to complete some integration techniques.
I found out that students who studied and understood differential calculus typically perform well in integral calculus. Generally, students pick up differential calculus quicker, and students who practice differentiation develop the insight necessary when they start learning integration.
What to read next:
- How Ordinary Differential Equations Differ from Partial Differential Equations.
- Is Vector Calculus Harder Than Regular Calculus?
- An Introduction to the Separation of Variables Method.
- A Level Math Vs. AP Calculus BC: Which one is harder?
In conclusion, differential and integral calculus are both important for students to understand. Differential calculus deals with rates of change, while integral calculus deals with sums over intervals or regions.
I also believe that both forms are essential for understanding complex mathematical problems in fields such as physics, engineering, and economics.
If you are a student, I encourage you to deepen your understanding of both mathematical concepts as both will make you well-equipped for successful college studies and might open up interesting career opportunities.