Pipe broken in engine bay, car sounds like motorbike

From the image that is the Exhaust Manifold.

The noise is likely comiing from a bad gasket between the bottom of the exhaust manifold and where the exhaust pipe connects to it.
With the engine running you should be able to feel the exhaust coming out at the connection. I usually hold a narrow sliver of paper near the connection and rev the engine to see if the exhaust blows the paper (which lets me know there is a leak ther).

If this is the case, it's usually not a hard fix, however the bolts which hold it on will often break (making it much more difficult). Spray them with penetrating oil before you begin work.
The gasket you'll need is # 31396 in the image.

Sorry about that. On the original picture I didn't notice the broken pipe (must be the resolution on my computer - surely not my old eyes )

Anyway, that pipe is the EGR pipe. It runs from the EGR valve to the Exhaust manifold. When you get the new pipe, change it when the engine is cool. Use penetrating oil (spray) on both ends of hte pipe so that they unscrew easily; without breaking or stripping out (spray to on and let it sit for about 30 minutes before working on it - it may need more than one treatment).

The part # I looked at is: "NISSAN OEM 14725F4500 Emission-Egr Tube, " which is the first diagram of EGR tubes.

But I am not sure which engine you have and the site doesn't mention an engine size.

Another way to be sure is to get the part number from the dealership and cross reference it at that site. They have a number listed there.

A plumber might be able to fabricate a pipe to fill in the gap (between the broken pieces).
Even if you have to remove the broken piece from the exhaust manifold, he could likely make one that would fit.

Also, The cost would be less than what a welder charges (at least that's the general rule in the U.S.)

There may even be a compression fitting large enough to fit that pipe and bring the pieces together again.

Electrical conduit with clamps on both ends is another option.

Good job, complete with nutrition information! Happy motoring, until next time. Send a picture of the final product, Ok?