91影视

"DEFINITE INTEGRALS"

The precise region of a function's graph on $[0,x]$.

• Riemann's sums are defined as the limit of the definite integrals.
• Definite integral properties

A study of topics connected to definite integrals.

The area between the horizontal axis and the graph of $f\left(x\right)$from 0 to x is accumulated by the accumulation function $A\left(x\right)$.

$A\left(x\right)={鈭�}_0^{x}f\left(x\right)dx$

Utilizing definite integrals to calculate the sums of the areas of small rectangles.

${鈭�}_0^{x}f\left(x\right)dx=\underset{n鈫�鈭�}{\lim }\underset{k=1}{\overset{n}{鈭�}}f\left(c_k\right)螖x$

$$\begin{gathered} 螖x=\frac{b-a}{n} \\ {c}_k=a+k螖x \end{gathered}$$

This makes it possible to determine the area under a curve.

This method of estimating the Riemann sums of the area between the curve and thex horizontal from 0 to x.

For definite Integrals, sum and constant multiple laws apply.

1. ${鈭�}_a^b\left[f\right(x)+g(x\left)\right]dx={鈭�}_a^{b}f\left(x\right)dx+{鈭�}_a^{b}g\left(x\right)dx$

2. ${鈭�}_a^{b}kf\left(x\right)dx=k{鈭�}_a^{b}f\left(x\right)dx$