(BQ) Part 2 book "Calculus with applications" has contents: Integration, further techniques and applications of integration, multivariable calculus, differential equations, probability and calculus. | 7 Integration Antiderivatives Substitution Area and the Definite Integral The Fundamental Theorem of Calculus The Area Between Two Curves Numerical Integration Chapter 7 Review Extended Application: Estimating Depletion Dates for Minerals Consumption of energy generated by the wind has increased from 70 trillion BTUs in 2001 to 1595 trillion BTUs in 2013. In this chapter, we will estimate wind energy consumption over this period using the definite integral, a mathematical concept that measures area under a curve. This same concept allows us to determine the distance a car has traveled, given its speed as a function of time; how much a culture of bacteria will grow; and how much consumers benefit by buying a product at the price determined by supply and demand. 395 395 19/07/16 3:46 PM 396 Chapter 7 Integration U ƒ1x2 = x5; find ƒ′1x2. p to this point in calculus you have solved problems such as In this chapter you will be asked to solve problems that are the reverse of these, that is, problems of the form ƒ′1x2 = 5x4; find ƒ1x2. The derivative and its applications, which you studied in previous chapters, are part of what is called differential calculus. The next two chapters are devoted to the other main branch of calculus, integral calculus. Integrals have many applications: finding areas; determining the lengths of curved paths; solving complicated probability problems; and calculating the location of an object (such as the distance of a space shuttle from Earth) when its velocity and initial position are known. The Fundamental Theorem of Calculus, presented later in this chapter, will reveal a surprisingly close connection between differential and integral calculus. Antiderivatives Apply It If an object is thrown from the top of the Willis Tower in Chicago, how fast is it going when it hits the ground? Using antiderivatives, we will answer
