maths problem (1 Viewer)

[barbecuedflava]

hey everyone i need help with this problem:

the rectangle PQRS has two vertices on the X-axis and two on the curve y = e^ negative x squared, where e is exponential.

it goes on to ask a couple of other questions e.g. max area but i need to know the sides of the rectangle first. i used 2x and e^ negative x squared as the length and breadth but i got a wrong answer.

so can anyone please tell me the sides of this rectange? thanks

 

[Iruka]

Well, e^(-x^2) is an even function, so if one of the corners of the rectangle was at the point (a,0), then there must be another corner at (-a,0), otherwise the shape won't be a rectangle. In this case, the area of the rectangle is 2ae^(-a^2) (assuming a>0).