Understanding Integrals in Algebra
Integrals are a fundamental concept in calculus, representing the accumulation of quantities and the area under curves.
What is an Integral?
An integral calculates the area under a curve or the accumulation of quantities.
It is the reverse process of differentiation.
Types of Integrals
- Definite integral: Has upper and lower limits and gives a number.
- Indefinite integral: Represents a family of functions (includes +C).
Basic Integration Rules
- \( \int x^n dx = \frac{x^{n+1}}{n+1} + C \) for \( n \neq -1 \)
- \( \int e^x dx = e^x + C \)
Applications of Integrals
Integrals are used to find areas, volumes, and solve real-world problems involving accumulation.
Practice Problems
- Find \( \int 3x^2 dx \).
- Evaluate \( \int_0^2 x dx \).
- Find the area under \( y = x^2 \) from \( x = 0 \) to \( x = 1 \).
📋
Contents
↑