Final answer:
The mathematical concept applied when sketching a solid whose volume is determined by an integral and evaluating that integral is integral calculus, a part of calculus focused on accumulation and areas or volumes.
Step-by-step explanation:
When asked to sketch a solid whose volume is given by an integral and then evaluate that integral, the mathematical concept being applied is integral calculus. Integral calculus is part of the broader field known as calculus, which deals with the mathematics of change and includes the study of limits, derivatives, integrals, and infinite series.
In particular, integral calculus involves the summing of infinitesimally small quantities, which can be used to find areas, volumes, and other concepts related to accumulation. A classic example of this in physics is computing the volume of a solid of revolution, where the volume can be found by integrating a cross-sectional area along an axis.
The act of integration itself adheres to the principles of dimensional analysis, ensuring the correctness of units throughout the computations.