The discussion focuses on the definite integral of the function ∫sin(2x)cos(x) from x=0 to x=π/4. The solution employs the double angle identity, transforming the integral into ∫2sin(x)cos²(x) and utilizing the substitution u=cos(x), leading to the evaluation of the integral as -2cos³(x)/3. The final result for the integral at x=π/4 is -1/(3√2), while the value at x=0 is calculated as (-1+2√2)/3√2. The participants confirm the correctness of the solution and engage in light-hearted banter.
PREREQUISITESStudents studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of definite integrals involving trigonometric functions.
)Jimbo57 said:
tiny-tim said:Hi Jimbo57!
(have a pi: π and try using the X2 button just above the Reply box
Fine down to …
… what about for x = 0 ?