Home page for accesible maths Math 101 Chapter 5: Integration

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5.12 Rules for combining integrals

Proposition

For integrable functions ff and gg, real numbers a,ba,b and cc, and a constant AA, the following hold:

∫(f⁢(x)+g⁢(x))⁢d⁢x=∫f⁢(x)⁢d⁢x+∫g⁢(x)⁢d⁢x;\int(f(x)+g(x))\,dx=\int f(x)\,dx+\int g(x)\,dx; i
∫A⁢f⁢(x)⁢d⁢x=A⁢∫f⁢(x)⁢d⁢x;\int Af(x)\,dx=A\int f(x)\,dx; ii
∫abf⁢(x)⁢d⁢x=-∫baf⁢(x)⁢d⁢x;\int_{a}^{b}f(x)\,dx=-\int_{b}^{a}f(x)dx; iii