What is the basic theorem of calculus Is integral and differential inverse operation

What is the basic theorem of calculus Is integral and differential inverse operation

The basic theorem of calculus generally refers to the Newton Leibniz formula for the calculation of definite integral,
It can be seen from the formula that when calculating definite integral, as long as the original function of the integrand is calculated and substituted into the end value of the interval to subtract, the definite integral value can be obtained. The calculation of the original function is closely related to the differential derivative, so the formula is called the basic theorem of calculus

Calculus basic theorem calculation!
∫ upper 2 lower 1 (x ^ 2-2x-3) / X DX
What is the derivative of (x ^ 2-2x-3) / x

First calculate (x ^ 2-2x-3) / x = x - 2 - 3 / x, and then calculate the original function according to the power function integral formula, that is [(x ^ 2) / 2 - 2x - 3ln | x |] '= x - 2 - 3 / X (x ^ 2) / 2 - 2x - 3ln | x | is the original function, so ∫ upper 2 lower 1 (x ^ 2-2x-3) / X DX is to substitute the upper limit into the value of the original function and then reduce it

The concept of definite integral and the basic theorem of calculus?

Warm tips
Definite integral is to find the area of function f (x) enclosed by graph line in interval [a, b]. That is, the area of graph enclosed by y = 0, x = a, x = B, y = f (x). This graph is called curved trapezoid, and the special case is curved triangle
Newton Leibniz formula if ∫_ a^b(f(x) dx ) =F(b)-F(a)