Integration In my biochemistry lab, integration is a critical tool of protein estimation, the method by which the amount of protein contained in a sample is approximated. The initial step is to split the sample into six or more parts. After applying some reagents, the fluids are run through a spectrometer. Once the results for each part of the sample are returned, calculus is used to get the total concentration. However, the usage differs from case to case.

Integration cont.:

Integration cont. The spectrometer measures the rate at which the proteins in the samples move across a membrane. The rates can then be transferred into a variety of mediums, such as a graph, depending on the situation. When working with caput, a segment of the studied protein, a graph is produced. The area under the graph is then integrated to find the total concentration. If the slope of the graph is not or nearly constant, Riemann sums are used to approximate. When working with cauda, another segment, the aforementioned technique will not work. Instead, one must integrate the general formula from zero to the total amount of sample. Before this however, the general formula must be broken into partial fractions, therefore bringing about the usage of partial integration. This method works well for only small amounts of sample, with larger amounts being covered by advanced computers.

Integration cont.:

Integration cont. Protein estimation is a highly important component of the studies of biochemistry researchers focusing on proteins by allowing them to formulate a tailored plan of attack. Without a good understanding of the concentrations of their samples, their efforts may be off and ultimately useless. When I perform protein estimation, the results contribute to the study of a certain protein in bull sperm with the end goal of creating male contraceptives. The study is ongoing and procedures such as protein estimation are very crucial.

Example:

Example =26.9405 lambda

Example:

Example lambda

Applied Parametric Equations:

Applied Parametric Equations Parametric equations represent the x and y coordinates of a set of points in terms of another variable, usually t In spaceflight, the trajectory of a space shuttle in the first five minutes after launch is dependent on the altitude, or h(T), and the down-range distance due-east, or R(T) h(T) = 2008 - 0.047(T^3) + 18.3(T^2) - 345T R(T) = 4680(e^(0.029T)) The speed of the shuttle along its trajectory can be calculated using the formula: The magnitude of the acceleration of shuttle can be calculated using the second derivatives of the parametric equations in the formula: | | The maximum acceleration can be found by setting the derivative of the magnitude of acceleration to zero Reference: NASA Goddard Space Flight Center

Applied Parametric Equations cont. This would be very useful to a NASA scientist coordinating the schematics of spaceflight operations. With the speed and acceleration, he/she could properly curate the course of a shuttle to ensure that astronauts reach their destinations as quickly as possible while consuming the least amount of resources possible, something the United States government would highly appreciate. The two values are extremely critical to their field as they are the tools by which conflicting gravitational patterns and relativity can be conquered to successfully reach destinations.

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