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zqz51911
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thanks,BvU said:So at the core you need $$ \int_0^l x\, sin(ax)\; dx {\rm \quad and \quad} \int_0^l x^2 \,sin(ax)\; dx$$ (with ## a = n\pi/l##) , right ?
Ever met these integrals ?
The process of completing an integral involves evaluating the integral expression and obtaining a numerical value. This is often done through integration techniques such as substitution, integration by parts, or using a table of integrals.
A definite integral has specific boundaries or limits of integration, while indefinite integrals do not. Definite integrals are used to find the area under a curve, while indefinite integrals are used to find a general solution to a differential equation.
The fundamental theorem of calculus states that the definite integral of a function can be calculated by finding an antiderivative of the function and evaluating it at the upper and lower limits of integration.
The most commonly used integral equation is the Riemann integral, which is used to calculate the area under a curve by dividing it into smaller rectangles and summing their areas.
Yes, integrals have numerous applications in various fields such as physics, engineering, economics, and statistics. For example, they are used to calculate work, velocity, and acceleration in physics, and to find areas and volumes in engineering and architecture.