Class notes calculus

CALCULUS

Calculus:-A branch of mathematics that deals with rates of change.

Example:- To calculate the change in velocity of a car rolling to a stop
at a red light. Calculus can help you figure out that change.

In calculus, a function is a relationship where each input (independent
variable) corresponds to exactly one output (dependent variable), often
represented as y = f(x).

Example:-Y= x2.Here y is dependent variable and x is independent
variable.

Differentiation and integration:-

Differentiation and Integration are branches of calculus where we
determine the derivative and integral of a function.

Differentiation:- The process of finding the ratio of a small change in
one quantity with a small change in another which is dependent on
the first quantity.

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Integration:- Process of finding the area under a curve of a function is
called integration.

NOTATION:- ∫Y dx,here Y is given function

Basic Integration Formulas
• ∫ xn dx = x(n + 1)/(n + 1)+ C
• ∫ 1 dx = x + C
• ∫ ex dx = ex + C
• ∫ 1/x dx = log |x| + C
• ∫ ax dx = ax /log a+ C
• ∫ ex [f(x) + f'(x)] dx = ex f(x) + C