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Related Concept Videos

Integration by Parts: Indefinite Integrals01:26

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Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...
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Definite integrals involving the product of two functions over a fixed interval can be evaluated using integration by parts. This method rewrites the integral as the difference of a product evaluated at the endpoints and a remaining definite integral that is often simpler to compute.A representative example is the definite integral of the inverse tangent function. Since there is no direct integration formula for arctan ⁡x, the integrand is rewritten as a product of arctan⁡ x and the...
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The water inflow rate into a storage tank is not constant but increases over time. Initially, the pump delivers water at a rate of 5 L/min. However, the inflow rate increases by 2 L/min for each additional minute due to rising pressure or system adjustments. This scenario can be described mathematically by a linear function:It is necessary to integrate the inflow rate function to measure the total volume of water added to the tank over time. The total water volume V(t) is obtained by performing...
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Related Experiment Video

Updated: Feb 11, 2026

Application of Biochip Microfluidic Technology to Detect Serum Allergen-specific Immunoglobulin E sIgE
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Magnetic nanochain integrated microfluidic biochips.

Qirong Xiong1, Chun Yee Lim2, Jinghua Ren3

  • 1School of Chemical and Biomedical Engineering, Nanyang Technological University, 70 Nanyang Drive, Singapore, 637457, Singapore.

Nature Communications
|May 3, 2018
PubMed
Summary
This summary is machine-generated.

Magnetic nanochains integrated into microfluidic biochips enable rapid mixing and specific bioseparation. This innovation allows for ultrasensitive detection of cancer biomarkers and bacteria in minimal sample volumes within minutes.

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Area of Science:

  • Biomedical Engineering
  • Nanotechnology
  • Analytical Chemistry

Background:

  • Microfluidic biochips offer potential for liquid analysis but lack integrated mixing, separation, and signal transduction.
  • Achieving rapid and ultrasensitive bioanalysis in simple microfluidic devices remains a significant challenge.

Purpose of the Study:

  • To develop an integrated microfluidic biochip utilizing magnetic nanochains for enhanced liquid analysis.
  • To overcome limitations in on-chip mixing, bioseparation, and signal transduction for faster, more sensitive bioassays.

Main Methods:

  • Fabrication of a microfluidic chip incorporating magnetic nanochains.
  • Utilizing magnetic nanochains as nanoscale stir bars for rapid liquid mixing.
  • Employing magnetic nanochains as capturing agents for specific bioseparation.
  • Integrating surface-enhanced Raman scattering (SERS) nanoprobes for signal transduction.

Main Results:

  • The magnetic nanochain integrated microfluidic chip demonstrated synergistic functions for mixing and bioseparation.
  • The planar chip design eliminated the need for complex built-in components.
  • The microfluidic assay enabled streamlined parallel analysis of multiple specimens.
  • Ultrasensitive identification and quantification of cancer protein biomarkers and bacterial species were achieved in 1 μl of body fluid within 8 minutes.

Conclusions:

  • Magnetic nanochains provide a versatile platform for developing simple, integrated microfluidic biochips.
  • This approach significantly improves assay kinetics and enables rapid, ultrasensitive bioanalysis.
  • The developed technology holds promise for advanced biomedical research and clinical diagnostics.