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Let y = e-t (a sin 3t + b cos 3t), where a, b are constants. Find dy/dt in simplest form, and hence by equating coefficients determine values for a, b so that dy/dx = 10e-t sin 3t. What is the average value of 10e-t sin 3t for 0 t pi ? (Leave your answer in terms of pi .)
Show transcribed image textLet y = e-t (a sin 3t + b cos 3t), where a, b are constants. Find dy/dt in simplest form, and hence by equating coefficients determine values for a, b so that dy/dx = 10e-t sin 3t. What is the average value of 10e-t sin 3t for 0 t pi ? (Leave your answer in terms of pi .)