Calculus Equations & Answers

S B Kizlik

• Publisher: QuickStudy Reference Guides
• Year: 2018
• ISBN:
  9781423240563
• Topic: Mathematik
• Subtopic: Infinitesimalrechnung

For every student who has ever found the answer to a particular calculus equation elusive or a certain theorem impossible to remember, QuickStudy comes to the rescue! This 3-panel (6-page) comprehensive guide offers clear and concise examples, detailed explanations and colorful graphs—all guaranteed to make calculus a breeze! Easy-to-use icons help students go right to the equations and problems they need to learn, and call out helpful tips to use and common pitfalls to avoid.

Integration

I. Area Under a Curve

1. If a function, f(x), is a curve graphed in the interval [a, b], then the area bounded by the curve, the x-axis, and the vertical lines containing the endpoints of the interval [a, b] may be approximated through the following:
   1. Rectangular methods
      1. Divide the interval into rectangles with equal width of

         b − a

         n

         .
      2. This results in n + 1 points on the x-axis.
      3. These points are x₀ = a, x₁ = a +

         b − a

         n

         , x₂ = a + 2

         	b − a
         	n

         , … , x_n = a + n

         	b − a
         	n

         .
      4. Find the sum of these n rectangles of equal width in the bounded region.
      5. Left-endpoint method
         1. The height of each rectangle is the vertical left side.
         2. The height of each rectangle is f(x_i) for 0 ≤ i ≤ (n – 1).
         3. The sum of these rectangle areas is

            b − a

            n

            [f(...