{"id":1577,"date":"2021-03-19T14:15:19","date_gmt":"2021-03-19T14:15:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus1\/?post_type=chapter&p=1577"},"modified":"2021-06-08T15:11:09","modified_gmt":"2021-06-08T15:11:09","slug":"introduction-to-the-definite-integral","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus1\/chapter\/introduction-to-the-definite-integral\/","title":{"raw":"Introduction to the Definite Integral","rendered":"Introduction to the Definite Integral"},"content":{"raw":"

What you\u2019ll learn to do:\u00a0Interpret definite integrals<\/h2>\r\n

In the preceding section we defined the area under a curve in terms of Riemann sums:<\/p>\r\n\r\n

[latex]A=\\underset{n\\to \\infty }{\\lim} \\displaystyle\\sum_{i=1}^{n} f(x_i^*)\\Delta x[\/latex].<\/div>\r\n \r\n

However, this definition came with restrictions. We required [latex]f(x)[\/latex] to be continuous and nonnegative. Unfortunately, real-world problems don\u2019t always meet these restrictions. In this section, we look at how to apply the concept of the area under the curve to a broader set of functions through the use of the definite integral.<\/p>","rendered":"

What you\u2019ll learn to do:\u00a0Interpret definite integrals<\/h2>\n

In the preceding section we defined the area under a curve in terms of Riemann sums:<\/p>\n

[latex]A=\\underset{n\\to \\infty }{\\lim} \\displaystyle\\sum_{i=1}^{n} f(x_i^*)\\Delta x[\/latex].<\/div>\n

 <\/p>\n

However, this definition came with restrictions. We required [latex]f(x)[\/latex] to be continuous and nonnegative. Unfortunately, real-world problems don\u2019t always meet these restrictions. In this section, we look at how to apply the concept of the area under the curve to a broader set of functions through the use of the definite integral.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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