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enriched a lot by the application of calculus.

1) Differential calculus

· Real number

· Function

· Limit

· Continuity

· Differentiation

· Second order derivative

2) Integral calculus

· Indefinite integral

· Method of substitution

· Integration by parts

· Integrals of some special form of functions

· Definite integral

3) Differential equation

· Order and degree of differential equations

· Differential equations of the first order and of the first degree

· Linear second order differential equations with constant coefficients

4) Application of calculus

· Significance of derivatives

· Tangent and normal

· Maxima and minima

· Definite integral as an area

· Velocity and acceleration

dy / dx = (x + 1) d / dx ( x – 1) + (x – 1) d/dx (x + 1)

= (x + 1) [ d / dx (x) – d / dx (1)] + (x – 1) [d/dx (x) + d/dx (1)]

= (x + 1) (1 – 0) + (x – 1) (1 – 0)

= (x+1) + (x -1)

= x + 1+ x – 1

= 2x

Therefore dy /dx = 2x

∫ x ^4 dx = x^ (4 + 1) / (4+ 1)

= x^5 / 5

Therefore ∫ x ^4 dx = x^5 / 5