It include computer chips that contain the central processing unit cpu and main memory

First, I'll focus on your question:

Is it correct to say that main memory (RAM) is a part of CPU?

Which seems prompted by the quoted assertion that:

The most important item of hardware is the CPU (Central Processing Unit)....It contains the processor and the main memory.

No, the CPU doesn't contain Main Memory.

Wikipedia defines the CPU as:

A central processing unit (CPU) is the electronic circuitry within a computer that carries out the instructions of a computer program by performing the basic arithmetic, logical, control and input/output (I/O) operations specified by the instructions. The computer industry has used the term "central processing unit" at least since the early 1960s. Traditionally, the term "CPU" refers to a processor, more specifically to its processing unit and control unit (CU), distinguishing these core elements of a computer from external components such as main memory and I/O circuitry.

The Processor is separate from main memory. Going all the way back to the the Intel 4004 created in 1971, the first microprocessor in which modern CPUs find their legacy, RAM (a.k.a. "Main Memory") has been a component external to the CPU.

Here's a block diagram of the 4004's successor, the Intel 8080, introduced in April 1974 (it's very similar to the Motorola 6800 released in August of the same year):

It include computer chips that contain the central processing unit cpu and main memory

Notice the pins labeled D0-7 and A0-15. The D pins are connected to the Main Memory and are used to transfer 8-bits of data to or from RAM at a time. This makes the Intel 8080 an 8-bit processor. The A pins are also connected to Main Memory, but are used to specify the address in memory that should be accessed by the next data read/write operation. These 16 address signals enable the processor to access up to 64KB of memory (216 = 65536 = 64KB).

The fact that memory is external to the processor is explained on page 263 of the book Code by Charles Petzold (published by Microsoft Press):

The 8080 is an 8-bit microprocessor that reads data from memory and writes data to memory 8 bits at a time. The chip includes eight signals labeled D0 through D7. These signals are the only ones on the chip that are both inputs and outputs. When the microprocessor reads a byte of memory, the pins function as inputs; when the microprocessor writes a byte to memory, the pins function as outputs. [emphasis mine]

Of course, an input (or output) signal is only necessary when a device connects to another device, in this case, Main Memory.

A further observation is that if Main Memory were integrated into the CPU, it would be impossible to expand the amount of memory available to the computer. It was recognized very early in the course of developing integrated circuits used for computers, in part to the extremely high cost of RAM at the time, that users may need to add more memory later. It would and continues to be a ludicrous idea to integrate Main Memory into the CPU.


Is it correct to say that CPU contains RAM? Or did it at any point in any form?

Yes, even early CPUs contained RAM (kinda).

That is, if by RAM we mean memory that can be accessed non-sequentially and is volatile, i.e. its content is lost when power is no longer applied.

On page 264 of Code we find a description of this "integrated memory":

In addition to the accumulator, the 8080 contains six registers that can also hold 8-bit values inside the microprocessor....Like the accumulator, the other six registers are latches; the processor can move bytes from memory into registers, and from registers back into memory.

So this is probably a stretch of the definition of RAM (and it's by no means Main Memory). However, it's obvious that the Registers in a CPU function as memory. For example, they are used to temporarily store values while the processor performs calculations using the Accumulator or store an address in Main Memory to read/write data to/from.

Modern processors now also include CPU Cache. This still isn't Main Memory though. When it comes to the CPU's cache and Main Memory, the former is used to store a copy of select data found in RAM in order to speed up processing time (by virtue of the fact cache memory is much faster than main memory). At no point does the CPU use its cache as a "permanent" storage location for data in the way Main Memory is used.


Side note:

As others have noted, the full of the text quoted in your question is a bit ambiguous. Particularly the bit I quoted earlier:

The most important item of hardware is the CPU (Central Processing Unit)....It contains the processor and the main memory.

Whether the text means to claim the CPU is the box in which all of the other "important" components are contained, or that it is the microprocessor, I can't say. Whatever the case, hopefully this answer helps provide an answer to what I believe your core question is: Whether or not main memory is part of the CPU.

What part of the computer contains the central processing unit?

The central processing unit (CPU), also called a processor, is located inside the computer case on the motherboard. It is sometimes called the brain of the computer, and its job is to carry out commands. Whenever you press a key, click the mouse, or start an application, you're sending instructions to the CPU.

What contains the processor chips in a computer?

The motherboard holds the CPU, RAM and ROM chips, etc. The Central Processing Unit (CPU) is the "brain" of the computer. It executes instructions (from software) and tells other components what to do. The Intel Pentium is a popular processor for IBM-PCs.

What is the name of the chip inside the computer that connects the central processing unit to the other primary components in the system?

The microprocessor contains the arithmetic, logic, and control circuitry required to perform the functions of a computer's central processing unit. The integrated circuit is capable of interpreting and executing program instructions and performing arithmetic operations.

What do you call the central processing unit on a chip?

In modern computers, the CPU is contained on an integrated circuit chip called a microprocessor.