IBDP Mathematics Applications & Interpretations HL Chapter 12 Notes

integral calculus


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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

After thoroughly understanding the concept of differentiation, we can now comprehend the idea behind integration. In this chapter, we will be studying integral calculus which is otherwise known as antidifferentiation meaning the reverse process of differentiation. Using integration, we can find the area under a particular graph using its function and limits if necessary. Under integration, there are different kinds of integral, some of which are Riemann Integrals. These integrals are a more general method to find the area under a graph which doesn’t follow quadratic functions. The next concept is with respect to antidifferentiation, which is the reverse of differentiation. Lastly, we will be learning the fundamental theorem of calculus which bridges a gap between differential calculus and definite integrals using Riemann Integrals.
In this chapter, just as we did in antidifferentiation, we can sometimes discover integrals by differentiation. In chapter 18 we developed a set of rules to help us differentiate functions more efficiently. However, finding antiderivatives can be difficult. Many functions simply do not have antiderivatives which can be expressed easily using standard functions. We construct some rules which allow us to integrate most of the function types we consider in this course. Further on in this chapter we also learn to find the constant of integration, c, if we are given a particular value of the function. In the next section we deal with integrals of functions which are composite with the linear functions, ax+b. Lastly, we learn to integrate by a method known as substitution. Integration by substitution is nothing but the reverse process of differentiating using the chain rule.