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**Integrals** are the inverse operation of differentiation. While derivatives measure rates of change, integrals deal with accumulation, adding up infinitesimally small quantities to find the total. Geometrically, a definite integral represents the area under a curve between two points. There are two main types of integrals: indefinite and definite. An **indefinite integral** (also known as an antiderivative) is a function whose derivative is the given function. It represents a family of functions, each differing by a constant. A **definite integral**, on the other hand, has limits of integration and yields a specific numerical value. The limits specify the interval over which you're finding the area under the curve. We will learn techniques for evaluating integrals, such as substitution, integration by parts, and trigonometric substitution. **Substitution** is often used to simplify the integrand by changing variables. **Integration by parts** is derived from the product rule of differentiation and is useful for integrating the product of two functions. **Trigonometric substitution** involves substituting trigonometric functions to simplify integrands involving square roots. The Fundamental Theorem of Calculus is a cornerstone, connecting differentiation and integration. It has two parts: The first part states that the derivative of an integral gives the original function. The second part states that the definite integral of a function can be found by evaluating the antiderivative at the limits of integration. This theorem allows us to calculate definite integrals efficiently. The applications of integrals are extensive, ranging from calculating areas and volumes to modeling physical phenomena and solving differential equations. These are so much more than just a math concept.