Pronunciation: /ˈdɛfənɪt ˈɪntɪɡrəl/
noun a mathematical concept used in calculus to determine the area under a curve between two specific points
A1 I am learning about definite integrals in my math class.
A2 To find the area under a curve, you need to calculate the definite integral.
B1 The definite integral of a function can be used to find the total accumulated quantity.
B2 Understanding how to evaluate definite integrals is essential in calculus.
C1 The concept of definite integrals is crucial in advanced mathematics and physics.
C2 Professionals in engineering often use definite integrals to solve complex problems.
verb none
A1 I am learning how to do definite integrals in my math class.
A2 She can calculate a definite integral using the trapezoidal rule.
B1 Students in the advanced calculus course are expected to understand definite integrals.
B2 The engineer was able to solve the problem by using a definite integral.
C1 The researcher used a complex algorithm to compute the definite integral of the function.
C2 The mathematician's groundbreaking work involved developing new techniques for evaluating definite integrals.
adjective none
A1 I heard the term 'definite integral' in my math class.
A2 The teacher explained how to calculate a definite integral using different methods.
B1 The student struggled with understanding the concept of definite integrals.
B2 She was able to solve the complex definite integral problem with ease.
C1 The mathematician presented a paper on the applications of definite integrals in physics.
C2 The professor's research focused on developing new algorithms for computing definite integrals.
adverb none
A1 I do not understand definite integral.
A2 She solved the definite integral using a simple method.
B1 The student calculated the definite integral of the function.
B2 The professor explained the concept of definite integral in great detail.
C1 The engineer used definite integrals to analyze the data.
C2 The mathematician's research focused on advanced techniques for evaluating definite integrals.
pronoun none
A1 I don't understand definite integrals.
A2 Can you explain how to solve a definite integral to me?
B1 The concept of definite integrals is essential in calculus.
B2 I have been practicing how to evaluate definite integrals for my math exam.
C1 Understanding the properties of definite integrals is crucial for advanced calculus studies.
C2 After years of studying mathematics, I have mastered the techniques of calculating definite integrals.
preposition none
A1 I am learning about definite integrals in my math class.
A2 The concept of definite integrals is starting to make sense to me.
B1 To calculate the area under a curve, you need to use a definite integral.
B2 Understanding how to apply definite integrals in real-world problems can be challenging.
C1 The use of definite integrals in physics equations is crucial for accurate calculations.
C2 Professionals in the field of engineering often rely on definite integrals to solve complex problems.
conjunction none
A1 I learned about definite integrals in my math class.
A2 To find the area under a curve, you need to calculate the definite integral.
B1 Understanding definite integrals is essential for solving advanced calculus problems.
B2 The concept of a definite integral can be applied to various real-life scenarios.
C1 Mathematicians use definite integrals to analyze complex functions and equations.
C2 When dealing with multidimensional data, mathematicians often rely on definite integrals for analysis.
interjection none
A1 Definite integral! I finally understand how to calculate it.
A2 I need to review definite integrals before the exam. Definite integral!
B1 The concept of definite integrals is crucial for understanding calculus. Definite integral!
B2 After studying for hours, I can now confidently solve definite integrals. Definite integral!
C1 The professor's explanation of definite integrals was so clear. Definite integral!
C2 I have mastered the technique of evaluating definite integrals. Definite integral!
article none
A1 A definite integral is a mathematical concept used to calculate the area under a curve.
A2 In basic calculus, students learn how to find the definite integral of simple functions.
B1 Understanding the definite integral is crucial for solving problems in calculus and physics.
B2 When dealing with complex functions, mathematicians often rely on numerical methods to evaluate definite integrals.
C1 The concept of a definite integral plays a key role in advanced mathematical analysis and modeling.
C2 Researchers in the field of computational mathematics constantly develop new algorithms for efficiently computing definite integrals.
formal The definite integral of a function f(x) over the interval [a, b] represents the signed area under the curve.
informal When you calculate the definite integral, you're basically finding the total area under the curve between two points.
slang Bro, the definite integral is like the legit total area under the curve from one point to another.
figurative Understanding the definite integral is like uncovering the hidden story beneath the graph of a function.
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