calculus problems

In calculus, and more generally in mathematical analysis, integration by parts is a rule that transforms the integral of products of functions into other, possibly simpler, integrals. The rule arises from the product rule of differentiation. The formula for Integration by Part..

Applications Differential Equations - As we have mentioned earlier that almost every branch of study deals with problems involving differential equation, in this section we solve few examples to exhibit the application of differential equation in various branches of knowledge.As we have m..

Definite Integrals - 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..

Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..

During the course of study of Mathematics, we must have come across several parts of inverse operations like (addition, subtraction) (multiplication, division) (forming an equation whose roots are given - solving a given equation) and so on. In practical situations, we may be interested to know the..

Let f be a continuous non-negative function defined on a closed interval [a, b]. Since the value of the function is non-negative, the graph of the function is a curve above X-axis. Let the graph of the curve be as shown in the figure.Let f be a continuous non-negative function defined on a closed i..

Definite Integral as a Limit of Sum - Let f be a continuous non-negative function defined on a closed interval [a, b]. Since the value of the function is non-negative, the graph of the function is a curve above X-axis. Let the graph of the curve be as shown in the figure.Let f be a continuous non-n..

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Let y = f(x) be a smooth curve and P(x,y) be a point on the curve. Equation of the tangent at (x 1 , y 1 ) in the curve y = f (x) is y - y 1 Equation of the normal at (x 1 , y 1 ) in the curve y = f (x) is If m = 0 the tangent at (x 1 , y 1 ) is parallel to x-axis. Angle of..

Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..