The discussion focuses on solving the improper integral of the function (2-x^4) over the interval from negative infinity to positive infinity. Participants clarify that u-substitution is unnecessary for this integral. Instead, the correct approach involves evaluating the limit of the integral as s approaches infinity: lim_{s→∞} ∫_{-s}^s (2-x^4) dx. The solution requires performing a standard antiderivative and substituting the limits accordingly.
Students studying calculus, particularly those focusing on integration techniques and improper integrals, as well as educators seeking to clarify these concepts for their students.
n!kofeyn said:\int_{-\infty}^\infty (2-x^4) \,dx
If so, you do not need u-substitution here. Also, to compute an improper integral of this form you need to evaluate:
\lim_{s\to\infty} \int_{-s}^s (2-x^4) \,dx