In both the differential and integral calculus, examples illustrat. Calculus i for computer science and statistics students. Exercises and problems in calculus portland state university. Ft f it dt for the antiderivative also called an indefinite integral. Once again, we will apply part 1 of the fundamental theorem of calculus. Before proving theorem 1, we will show how easy it makes the calculation ofsome integrals.
Explain the relationship between differentiation and integration. Use the fundamental theorem of calculus, part 1, to evaluate derivatives of integrals. Fundamental theorem and denite integrals the fundamental. Use the fundamental theorem of calculus, part 2, to evaluate definite integrals. This is nothing less than the fundamental theorem of calculus. Understanding basic calculus graduate school of mathematics. The fundamental theorem tells us how to compute the derivative of functions of the form r x a f t dt. State the meaning of the fundamental theorem of calculus, part 2. F t f it dt for the antiderivative also called an indefinite integral. The fundamental theorem of calculus calculus volume 1. Your students will have guided notes, homework, and a content quiz on fundamental theorem of c. Accompanying the pdf file of this book is a set of mathematica. Pdf chapter 12 the fundamental theorem of calculus.
Use part i of the fundamental theorem of calculus to nd the derivative of the following functions. Mean value theorem for integrals university of utah. There are free tables of integrals available in pdf format. The fundamental theorem of calculus and definite integrals lesson. The fundamental theorem of calculus if we refer to a 1 as the area correspondingto regions of the graphof fx abovethe x axis, and a 2 as the total area of regions of the graph under the x axis, then we will.
Your ap calculus students will evaluate a definite integral using the fundamental theorem of calculus, including transcendental functions. Theorem if f is a periodic function with period p, then. State the meaning of the fundamental theorem of calculus, part 1. Use part ii of the fundamental theorem of calculus to evaluate the following integrals or explain why the theorem does not apply.