Alternative method

( 1) ?

(2)x=ψ(t) is single-valued differentiable in [α, β].

(3) When α≤t≤β, a≤ψ(t)≤b, and ψ (α) = A, ψ (β) = B.

then what

2. Partial integration method

Let u = u (x) and v = v (x) both be derivable on the interval [a, b], and u ′, v ′ ∈ r ([a, b]), then there is a partial integral formula:

The mathematical definition of definite integral: If the function f(x) is continuous on the interval [a, b], divide the interval [a, b] by n with the fractional point xi? Between cells, take a little ri(i= 1, 2,3) [xi-1,xi] between each cell? ，n)？ And the formula f(r 1)+...+f(rn)? When n approaches infinity, the above sum approaches a constant A, which is called y=f(x)? Is the definite product on the interval /ab? f(x)？ dx？ Namely. /ab？ f(x)？ dx？ = limn & gt00? [f(r 1)+...+f(rn)]，？ Here, a? With what? B is called the lower integral limit and the upper integral limit, and the interval [a, b]? It's called the integral interval, the function f(x)? It's called integrand function, x? It's called an integral variable, f(x)dx? It is called the integrand function.

Geometric definition: can be understood as in? On the coordinate plane of Oxy, the area value of the curve trapezoid surrounded by curve y=f(x), straight line x=a, x=b and X axis. (a definite actual value)