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If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..

If f (x) is a function continuous on [a, b] then Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(b) ..

The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer scienc..

After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class..

First Fundamental Theorem of Integral Calculus Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined ..

Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a he..

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..

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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..