# Ibernoulli; Ibp - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Description:
Determines the basis of the intersection between two vector spaces.
Matrices, !Ø L
Access:
Input:
Two lists of vectors
Output:
A list of vectors.
Flags:
Exact mode must be set (flag –105 clear).
Example:
Find a vector of a basis of the intersection of the vector sub-spaces defined by [1, 2] and [2, 4]
Command:
IBASIS({[1,2]}, {[2,4]})
Result:
{[1,2]}
BASIS

## IBERNOULLI

Type:
Function
Description:
Returns the nth Bernoulli number for a given integer n.
Arithmetic, !Þ
Access:
Input:
Level 1/Argument 1: an integer.
Output:
Level 1/Item 1: The corresponding nth Bernoulli number for the integer. For numbers greater
than about 40 the calculation can take a long time.
Flags:
Numeric mode must not be set (flag -3 clear).

### IBP

Type:
Command
Description:
Performs integration by parts on a function. The function must be able to be represented as a
product of two functions, where the antiderivative of one of the functions is known:
f(x) = u(x).v'(x)
Note that the command is designed for use in RPN mode only.
P
Access:
CALC
Input:
Level 2: The integrand expressed as a product of two functions,
Level 1: The antiderivative of one of the component functions, v(x).
Output:
Level 2: u(x)v(x)
Level 1: -u'(x)v(x)
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Use integration by parts to calculate the following:
x
cos
x
Command 1: Apply the IBP command in RPN mode:
Level 2:
Level 1:
Result:
Level 2:
Level 1:
Command 2: Apply the INTVX command to level 1,
Result:
Level 2:
Level 1:
Command 3: Press + to add the result to the value at level 2 to obtain the final result.
VECTOR
INTEGER
or Calculus, !Ö
x d
X*COS(X)
SIN(X)
SIN(X)*X
-SIN(X)
SIN(X)*X
COS(X)
L
&
DERIV
INTEG
-SIN(X)
Computer Algebra Commands 4-39
u(x).v'(x)