Maclaurin Integration and Term-by-Term Integration

Question

1.)

a-Evaluate the integral from 0 to 1/2 of ln(1+x)dx with an accuracy of 10^-4 using techniques of integration and a calculator.

b- Now approximate the integral from 0 to 1/2 of ln(1+x)dx to an accuracy of 10^-4 using the Maclaurin series of ln(1+x) and term-by-term integration. You will have to figure out how many terms of the series must be used. Are the answers to a) and b) very similar numbers?

Answer 1

I=∫ln(1+x)dx

0

I=x ln(1+x)−∫dx+∫1/(1+x)dx =2.0273integral

.5 =0 differential