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Example: Integrating a Function Using the Power Rule ∫ √t ( 1 + t ) d t . Show Solution ∫14t(1+t)dt=∫14t1/2(1+t)dt=∫14(t1/2+t3/2)dt. ∫14(t1/2+t3/2)dt=(23t3/2+25t5/2)|14=[23(4)3/2+25(4)5/2]−[23(1)3/2+25(1)5/2]=25615. ...
An example of initial values for this second-order equation would be y(0)=2y(0)=2 and y′(0)=−1y′(0)=−1. These two initial values together with the differential equation form an initial-value problem. These problems are so named because often the independent variable in the ...
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1.a method of calculation, esp. one of several highly systematic methods of treating problems by a special system of algebraic notations, as differential or integral calculus. 2.a stone, or concretion, formed in the gallbladder, kidney, or other part of the body. ...
For example, the Greek geometerArchimedes(287–212/211bce) discovered as an isolated result that the area of a segment of aparabolais equal to a certain triangle. But with algebraic notation, in which a parabola is written asy=x2, Cavalieri and other geometers soon noted that the area betw...
Learn what optimization means in calculus. Discover the optimization problems. Learn the steps to solve the optimization problems. See optimization...
As a simple example, let’s take 3/2. Subtract a multiple of the denominator from the numerator.The denominator: the denominator (bottom number) is 2, so multiples of 2 are 2, 4, 6, 8…; The biggest multiple of 2 we can subtract from the numerator is just 2 · 1 = 2. ...
Taylor’s Theorem: Definite, Step by Step Example See also:Sequence and series(main page) Volume: Volume of a Cone Volume of an Egg Cylindrical Shell Formula Washer Method Word Problems Index TI 89 Calculus: Step by Step The Tautochrone Problem / Brachistrone Problem ...
Avideo of each lessonwith crystal-clear explanations of each example...great for absent or struggling students. Unit reviews and cumulative reviews with fully worked keys Unit tests with fully worked keys Quizzes with fully worked keys Extensive "how to" Calculator Appendix...each with a video...