HP 35s Scientific 8  (), Example: Specifying Accuracy, Example: Changing the Accuracy, The uncertainty of the approximation of the integral

Example: Specifying Accuracy.

With the display format set to SCI 2, calculate the integral in the expression for Si(2) (from the previous example).

Keys:Display:

8  ()

￿  



X	
	∫ 
	



Description:

Sets scientific notation with two decimal places, specifying that the function is accurate to two decimal places.

Rolls down the limits of integration from the Z–and T–registers into the X–and Y–registers.

Displays the current Equation. The integral approximated to two decimal places.The uncertainty of the approximation of the integral.

The integral is 1.61±0.0161. Since the uncertainty would not affect the approximation until its third decimal place, you can consider all the displayed digits in this approximation to be accurate.

If the uncertainty of an approximation is larger than what you choose to tolerate, you can increase the number of digits in the display format and repeat the integration (provided that f(x) is still calculated accurately to the number of digits shown in the display), In general, the uncertainty of an integration calculation decreases by a factor of ten for each additional digit, specified in the display format.

Example: Changing the Accuracy.

For the integral of Si(2) just calculated, specify that the result be accurate to four decimal places instead of only two.

Integrating Equations 8-7