Page 299 - DMTH401_REAL ANALYSIS

Unit 24: Fundamental Theorem of Calculus

24.5 Review Questions Notes

1. Find the primitive of the function f defined in [0, 2] by

Î
ì x if x [0,1]
f(x) = í
Î
î I if x [1,2]
2 ì x if x ¬ [0, 1]
ò
2. Find f(x) dx where f is the function given in f(x) = í
0 î 1 if x ¬ [1, 2]
b
n
3. Evaluate x dx where n is a positive integer.
ò
1
Answers: Self Assessment
x
1. intermediate value property 2. F(x) = ò f(t) dt, x E[a,b].
a
3. antiderivative

24.6 Further Readings

Books Walter Rudin: Principles of Mathematical Analysis (3rd edition), Ch. 2, Ch. 3.
(3.1-3.12), Ch. 6 (6.1 - 6.22), Ch.7(7.1 - 7.27), Ch. 8 (8.1- 8.5, 8.17 - 8.22).

G.F. Simmons: Introduction to Topology and Modern Analysis, Ch. 2(9-13),
Appendix 1, p. 337-338.
Shanti Narayan: A Course of Mathematical Analysis, 4.81-4.86, 9.1-9.9, Ch.10,Ch.14,
Ch.15(15.2, 15.3, 15.4)
T.M. Apostol: Mathematical Analysis, (2nd Edition) 7.30 and 7.31.
S.C. Malik: Mathematical Analysis.

H.L. Royden: Real Analysis, Ch. 3, 4.

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