Exponential curves + area
Knowledge bridge
Step 1: set y = e^{-x} equal to y = e^{-x}(sin x + cos x) and cancel the common exponential to get a trig equation for intersection abscissae α_i. Step 2: order those roots and set up the definite integral of the difference of the two curves between α_1 and α_4 for the enclosed area β. Step 3: simplify the given log expression in β to a clean numerical value.
Why it feels hard
The stem hides trig solving inside an exponential envelope; students often integrate before finding exact limits.
What to practise
Drill ‘cancel common positive factor → trig roots → area integral’ as one reflex chain.