Each element, $r\,d\theta$, is not $r$ away from the central axis. As you move from the central axis not only does each element have a greater force exerted on it, $B\,i\,r\,d\theta\,\sin \theta$, the element is also a greater distance from the axis, $r\,\sin \theta$ where $\theta$ is the angle subtended between the central axis and the element.
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