integration by parts formula

Definite Integrals Animation..

Definite Integrals Animation..

Animation Indefinite Integrals..

Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..

Animals are different from plants because of their ability of locomotion. This ability probably developed as they have to search for food, unlike the plants that are autotrophic. Since they move from place to place, the animals have to continuously encounter changes in their environment. All ..

Let y = f (x) be a curve. The area bounded by y = f (x), x-axis and the ordinates at x = a and x = b is given byLet y = f (x) be a curve. The area bounded by y = f (x), x-axis and the ordinates at x = a and x = b is given by (ii) The area bounded by the curve x = f (y) y = axis and the abscissae at..

The definition, , can be explained in another way also. We rewrite above definition as Here the first term is hf (a). It is the area of the rectangle marked as 1 in figure below (because h and f (a) are the adjacent sides of this rectangle). Similarly, the second term hf (a+h) is the area of the re..

The area bounded by the curve y = f(x), x-axis, and the ordinates at The area bounded by the curve x = f(y), y - axis and the abscissas If f(x) is continuous in [a,b] and crosses the x-axis at x = c in (a, b) then the area bounded by the curve, x - axis and x = a and x = ..

Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..

..