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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
There is a committee to be selected comprising of 5 people from a group of 5 men and 6 women. Whether the selection is randomly done then determines the possibility of having the g
Find out the hydrostatic force on the following triangular plate that is submerged in water as displayed. Solution The first thing to do here is set up an axis system
Reduction formulae Script for Introduction: First let us know what is meant by reduction formula. In simple words, A formula which expressess(or re
the operations of cyclic permutations
sin45
The index of industrial production This is a quantity index compiled by the government. This measures changes in the volume of production in main industries. The index is a ex
x+2y^2=63 and 4x+y^2=0; Find the area of the regions enclosed by the lines and curves.
A class has 175 learners. The given table describes the number of learners studying one or more of the subsequent subjects in this case Subjects
In this case, the first point we have to remember is that we do not get a single value when we add two or more terms which are unlike in nature. This certainly ob
A farmer's rectangular field has an area in which can be expressed as the trinomial x2 + 2x + 1. In terms of x, what are the dimensions of the field? Because the formula for th
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