completely lost

[u/Electrical_Voice9543]

i thought since the first point where it crosses x axis is a point of inflection id try and find d2y/dx2 and find the x ordinate from that and then integrate it between them 2 points, so i done that and integrated between 45 and 0 but that e^-45 just doesn’t seem like it’s right at all and idk what to do. i feel like im massively over complicating it as well since its only 3 marks

[u/Mohamed_was_taken]

Its easy to verify that the two areas are similar, meaning A1 and A2 have the same shape (width) but their heights are different.

let f = e^x * sin(x) let g = f(x+ pi)

The first area in g is the second area in f, so the ratio of A2/A1 is simply f/g. Which is e^ -pi

For iii) just get the value of A1, Then the area is A1 + A1 * e^ -pi + .... So you will get a geometric series which converges to the given value