MATH 1ZB3 Lecture 1: Integration Review & Techniques
8 Jan 2019
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R f (x)dx, the inde nite integral of f(x) is a function f(x) such that f"(x)=f(x). Some basic integrals: n+1 xn+1: r xndx = 1, r 1 x dx = ln|x, r exdx = ex, r cosxdx = sinx, r sec2xdx = tanx, r. You can verify your answers by di erentiating your answer to see if you get back to the original question. For example: d dx (sinx + c) = cosx. The fundamental theorem of calculus asserts r b is an antiderivative of f(x). Example: a f (x)dx = f (x)(cid:12)(cid:12)(cid:12) a b where f(x) Let u = x3 ,then du = 3x2dx. 3 sinudu cosu + c cos(x3) + c. Let u = x and dv = ex, then du = dx and v = ex. Or: let x=0 then a=-1, let x=1 then b=1. = ln|x| + ln|x 1| + c. Z let x = sin(u) then dx = cos(u)du.
