integration by parts formula

Question 1 - Question: Where does the brook begin? Answer: Place frequented by coots and hern..

Differentiation deals with the rate of change while integration deals with the total change. The definite integrals are evaluated in problems relating to plane, areas, areas and volumes of solid of revolution etc. In this chapter, we confine ourselves to properties of de..

Introduction - Integration and differentiation are a pair of inverse operations. So far, from a given function, we have been finding its derivative but the question arises: what is the function whose derivative is known? If the derivative of a function is given, then the function itself i..

The expression f(x) dx is read "the indefinite integral of f(x) with respect to x," and stands for the set of all antiderivatives of f. Thus, f(x) dx is a collection of functions ; it is not a single function , nor a numbe..

By method of completing squares ax 2 + bx + c is expressed as A 2 + X 2 or X 2 - A 2 and the integral reduces to which can be evaluated using the standard integrals..

Prove that: ..

Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..

Integration by Partial Fractions - Before using this technique of integration, let us recall what we have learnt about partial fracti..