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A comprehensive introduction to calculus, a fundamental branch of mathematics. It covers the main concepts of limits, functions, derivatives, integrals, and infinite series. The document delves into the two main branches: differential calculus and integral calculus, and presents key definitions, notations, and basic rules for derivatives and integrals. It also includes example problems for finding derivatives and evaluating integrals. This resource is ideal for students studying informatics engineering at gunadarma university in 2024.
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Overview of Calculus Calculus is a branch of mathematics focused on the concepts of limits, functions, derivatives, integrals, and infinite series. It is divided mainly into two branches:
o Sum Rule: 𝑑 𝑑𝑥 [f(x) + g(x)] = f′(x) + g′(x) o Product Rule: 𝑑 𝑑𝑥 [f(x) g(x)] = f′(x)g(x) + f(x)g′(x)
2. Evaluating an Integral Problem : Evaluate the integral ∫ (4x^3 − 2 x + 6) dx Solution : 1. Integrate each term separately. 2. ∫ 4x^3 dx − ∫ 2x dx + ∫ 6 dx 3. Using the power rule for integrals: o ∫ 4x^3 dx = 4 ⋅ 𝑥^3 +^1 3 + 1 = x^4 o ∫ 2x dx=2 ⋅ 𝑥^1 +^1 1 + 1 = x^2 o ∫ 6 dx = 6x 4. Combine the results and add the constant of integration C: o x^4 – x^2 + 6x + C