Integrals in Calculus

Integrals in Calculus

Nnadozie Okarazu

Integrals

Integrals are antiderivatives: they find the original function that when differentiated will give you that same derivative. In a way it is like saying, “what came first, the chicken or the egg?” (except, the answer to the question in a calculus class is either indefinite or finite).

Example

Given    find the indefinite integral or the general solution.

Solution

∫2sin(x)cos(x)dx = ∫sin(x)cos(x) + sin(x)cos(x) dx
Let “u” = sin(x)
du = cos(x)dx
Therefore,
∫sin(x)cos(x) dx + ∫sin(x)cos(x) dx = ∫u du + ∫u du
y = u^2/2 + u^2/2 + C
Substitute “u” as sin(x)
y = sin^2(x) + C
 
Source: Math Tutor