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MATHEMATICS, SURVEYING, TRANSPORTATION ENGINEERING, AND CONSTRUCTION presented by: Gwyneth B. Hermoso Kippap Civil Engineering INTEGRAL CALCULUS
A logo with a white letter Description automatically generated LECTURE OUTLINE • Direct Integration • Integration Techniques • Multiple Integration • Areas by Integration DAY 12: INTEGRAL CALCULUS The grind is temporary. The license is forever.
DAY 12: INTEGRAL CALCULUS DIRECT INTEGRATION The antiderivative of a function is the function whose derivative is the function itself. For example, when differentiating the function f(x) = x 5 , then the result is f ′ (x) = 5x 4 . Therefore, f x = x 5 + C is the antiderivative of f ′ (x) = 5x 4 , where C is an arbitrary constant. A logo with a white letter Description automatically generated The grind is temporary. The license is forever.

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