Definite and indefinite integrals

Definite and indefinite integrals are fundamental concepts in calculus, each serving distinct purposes in mathematical analysis. Indefinite integrals, also known as antiderivatives, represent families of functions whose derivatives yield a given function. On the other hand, definite integrals compute the accumulated area under a curve over a specific interval, providing precise numerical values. Together, these concepts form the backbone of integral calculus, facilitating the analysis of functions, computation of areas, and solving a wide array of mathematical problems. Understanding their distinctions and applications is essential for mastering the intricacies of calculus.