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Difference between Differentiation and Integration. Key Difference : In calculus, differentiation is the process by which rate of change of a curve is determined.
Integration is just the opposite of differentiation. It sums up all small area lying under a curve and finds out the total area. Image Courtesy: maths. Comments Thanks! Crystal Clear. Your name. Plain text. This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Nevertheless, it is remarkable to highlight that both differentiation is essential calculus concepts that make life easy. One of the main application of integration is calculating the areas of curved surfaces, calculating the volume of objects, and calculating the central point among other functions. On the other hand, differentiation concept is significantly used in calculating instantaneous velocity and used in determining whether a function is increasing or decreasing accordingly.
This is a clear demonstration of how the two concepts are applied in the lives of individuals. The other difference between integration and differentiation is the role they play when it comes to any given function under investigation. According to mathematicians, differentiation significantly helps in determining the speed of the function by helping in the calculation of instantaneous velocity.
On the other hand, integration is concerned with determining the distanced travelled by any given function. The area under the curve is estimated to be equivalent to the distance travelled by the function. Integration algebraic expression helps in calculating the area under the curve, which amounts to the distance travelled by the function. It is also worth noting that differentiation and integration have different algebraic expressions, which are used in the calculation.
This explains why the two calculus concepts will always provide different results. The derivative of a function f x concerning the variable x and according to the product rule will be defined as:. On the other hand, the integration formula or the integral area under the curve can be calculated by use of the formula:. The other method of comparing integration to differentiation is by specifically explaining how each function realizes its results.
Integration determines the outcome of a specific function by adding the aspects associated with calculation. On the other hand, differentiation determines instantaneous velocity and the speed of the function through division. Difference Between Differentiation and Integration. Difference Between Similar Terms and Objects.
MLA 8 Morgan, Jecinta. Name required. Email required. Please note: comment moderation is enabled and may delay your comment. The Differential 2. Antiderivatives and The Indefinite Integral 3. The Area Under a Curve 4. The Definite Integral 5. Trapezoidal Rule 6. Riemann Sums 6b. Fundamental Theorem of Calculus Applet 7. Integration Mini-lectures 7a. The Differential 7b. Difference Between Differentiation and Integration 7c. Integration by Substitution 7e.
Difference Between Definite and Indefinite Integrals 7f. Home » Integration » 7b. Difference Between Differentiation and Integration. Related lessons on IntMath This video explains the difference between: Differentiation
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