Lots of derivative formulas, the product rule, the chain rule, implicit differentiation, the fact that integrals and derivatives are opposites, Taylor series, just a lot of things like that. And my goal is for you come away feeling like you could have invented calculus yourself. That is, cov...
Ch 16.Applications of Integrals Ch 17.Using the Fundamental Theorem of... Ch 18.Applying Integration Techniques Ch 19.Approximation of Definite... Ch 20.Understanding Sequences & Series Ch 21.Series of Constants Ch 22.Taylor Series Ch 23.Using a Scientific Calculator for... ...
4有些同学对于有个题目是不是应该absolute value an integral不确定,记住在计算distance的时候我们会需要absolute value an integral,we don’t have to do that for regular integrals。考到的那道题目不需要absolute value it。 5在FRQ的第5题考查了use...
4.Substitution Rule for definite Integrals (du= g’(x)dx) (u = g(x))【一定要先把原函数代进去再求它的导】 5.求积分函数的导数 1.灵活运用Substitution Rule,不要出错!!! 2.dx中的x是虚拟变量,不是自变量!!!只要保持’f(u1)du2’中的u1 , u2一致就行,如果不一致需要用Substitution Rule 3....
7. Improper integrals: for integral with one end or both ends at infinity of f(x) is undefined, use a letter b to represent it and finish the integral. Then calculate lim F(x) from b to another number Unit VIII. Parametric, Vector,andPolar functions ...
Let U and V be functions of x. From the product rule:d(UV)/dx = V (dU/dx) + U (dV/dx) Integrating both sides with respect to x and rearranging,∫ U(dV/dx).dx = UV - ∫ V (dU/dx) dx Given some product to integrate, we arrange for U and dV to make the integral on ...
, whose integrals are and respectively. If you closely examine the physically different, yet mathematically equal functions, you can notice that in most cases the integrable form is quite evident�and can easily be found with a few quick simplifications such as: ...
Ultimately, calculus is the mathematical study of how things, usually functions, change. They utilize limits, sequences, series, derivatives, differentials, and integrals in order to analyze functions and how they change. Calculus also has many real-world applications:View...
Mean Value Theorem for Integrals: b f (x ) d x = f (c ) (b ? a ) for some c a in (a , b). 18. Area Bounded by 2 Curves: x2 Area = ( f (x ) ? g (x ))d x , x1 where f (x ) ≥ g (x ). 19. Volume of a Solid with Known Cross Section: b V = A(x...
Special emphasis is given to the product rule for arbitrary order derivintegrals. The Riemann‐Liouville fractional integral R–αf and the Weyl fractional integral W–αf (α > 0) are discussed in some detail. It is shown that these integrals can be expressed as the convolution. The Mellin...