MATH 105 Lecture Notes - Lecture 8: Antiderivative, 32X

• School: UBC
• Department: Mathematics
• Course: MATH 105
• Professor: LIU, KEQIN

Document Summary

Given a function, f(x), an anti-derivative of f(x) is any function f(x) such that. If f(x) is any anti-derivative of f(x) then the most general anti-derivative of f(x) is called an indefinite integral and denoted, In this definition the is called the integral symbol, f(x) is called the integrand, x is called the integration variable and the c is called the constant of integration. The process of finding the indefinite integral is called integration or integrating f(x) . If we need to be specific about the integration variable we will say that we are integrating f(x) with respect to x. The indefinite integral is: x^4+3x 9 dx = 15x^5+32x^2 9x+c. Kf(x) dx = k f(x) dx where k is any number. So, we can factor multiplicative constants out of indefinite integrals. F(x) dx = f(x) dx this is really the first property with k= 1 and so no proof of this property will be given.