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All the integrals below are understood in the sense of the Lebesgue.
(1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]. Then
(2) Assume that f is integrable over [0; 1]. Show that
is di erentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
Maths For Fun : Often, when I have time on my hands, I try to solve interesting mathematical questions of the following kind. Sometimes my friends and I create the problems, and
Integrals Involving Quadratics To this point we have seen quite some integrals which involve quadratics. Example of Integrals Involving Quadratics is as follow: ∫ (x / x 2
Calculate average speed of a train: What is the average speed of a train which completes a 450-mile trip in 5 hours? Solution: Using Equation 15: V av = s/t V a
how to find
Volumes of Solids of Revolution / Method of Cylinders In the previous section we started looking at determine volumes of solids of revolution. In this section we took cross se
Problems Involving Motion - Word Problems: How far can a car travelling at a rate of 52 miles per hour travel in 2½ hours? Solution: Using Equation 13: s = vavt
PROOF OF VARIOUS INTEGRAL FACTS/FORMULAS/PROPERTIES In this section we've found the proof of several of the properties we saw in the Integrals section and also a couple from t
2x40 420x4 7x240 84x20 Explain how three expressions are equivalent.
What fraction could you add to 4/7 to get a sum greater than 1
if theta is a positive acute angle and 2sin theta +15cos square theta=7 then find the value of cot theta
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