Find the equation of the curve that passes through the point (x, y) = (0, 0) and has an arc length on the interval x is between 0 and pi over 4 inclusive given by the integral the integral from 0 to pi over 4 of the square root of the quantity 1 plus the cosine squared x, dx . (5 points)

Step-by-step explanation:

The curve passes through the point (x, y) = (0, 0) and has an arc length on the interval [0, π/4] given by the integral:

And we want to find the equation of the curve.

Recall that arc length is given by:

Rewrite our original integral:

So:

It follows that:

Using the initial condition:

The equation for our curve is:

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0