HP15C HP42S integration of trig differs in *rad and *deg

[Dieter]

(04-27-2018 07:05 PM)hansepie Wrote:  f(x) = sin(x)

When performing integration in RAD=mode lower limit 0 and upper limit PI/2 it returns 1.0000.

That's the correct result: –cos(pi/2) – –cos(0) = 0 – (–1) = 1.

(04-27-2018 07:05 PM)hansepie Wrote:  When performing integration in DEG-mode lower limit 0 and upper limit 90 it returns 57.2960.

That's the correct result as well.

The antiderivative of sin(x) is –cos(x) – but for x in radians!

If you use degrees you actually integrate sin(x° · pi/180°). Here the antiderivative is –180/pi · cos (x°). This leads to a result of 180/pi = 57,2958.

(04-27-2018 07:05 PM)hansepie Wrote:  I expected the same results.

Then you should try GRAD mode as well. This yields 200/pi = 63,662. ;-)

(04-27-2018 07:05 PM)hansepie Wrote:  HP-42S and HP-15C give the same results.

I hope so. ;-)

(04-27-2018 07:05 PM)hansepie Wrote:  What do I miss?

For the mathematical explanation see above.

Here's an idea that may help understand what's going on here: Imagine the graph of sin(x) between 0 and pi/2 or 0 and 90°. The integral is the area between graph an x-axis. The vertical height is the same in both cases: it starts at 0 and finally reaches 1. But the horizontal width is very different: in the one case the area is only 1,57 units wide while in the other case it's a whopping 90 units! So it's clear that the area (i.e. the integral) must be much greater. Actually it is greater by a factor of 90/1,57... = 57,2958.

And finally: welcome to the forum. :-)

Dieter