Hey, I’m Integration! Rumours are, that I’m the nightmare of students. They scream upon hearing my name. But did you know that all I do is join things? Like if you cut a paper in a lot of strips and then place them side by side, that’s an indefinite integral. Yes, that’s what I do. Don’t believe me? Why don’t you go through the integrals concepts below to see how right I am?
Sections
- Fundamental Theorem of Calculus
- Introduction to Integration
- Properties of Indefinite Integrals
- Properties of Definite Integrals
- Definite Integral as a Limit of a Sum
- Integration by Partial Fractions
- Integration by Parts
- Integration by Substitutions
- Integral of Some Particular Functions
- Integral of the Type e^x[f(x) + f'(x)]dx
FAQ on Integrals
Question 1: What are integrals in calculus?
Answer: An integral refers to a mathematical object which can be interpreted as an area or a generalization of area. Integrals, along with derivatives, refer to the fundamental objects of calculus. Moreover, the Riemann integral is the simplest integral definition and the only one which we commonly encounter in physics and elementary calculus.
Question 2: Can definite integrals be negative?
Answer: Yes, definite integrals can be negative. Integrals are used to measure the area between the x-axis and the curve in problem over a particular interval. Thus, if all of the areas within the interval will exist above the x-axis yet below the curve then the result will be positive.
Question 3: What are integrals used for?
Answer: We can use integrals for computing the area of a two-dimensional region which has a curved boundary, in addition to computing the volume of a three-dimensional object which has a curved boundary. We can calculate the area of a two-dimensional region by making use of the aforesaid definite integral.
Question 4: Can you multiply two integrals?
Answer: Yes, we can multiply two things together when we have defined a multiplication operation. However, for now, there is no any operation defined over integrals that would let us consider multiplying two integrals together.