Integral is the core concept in calculus and mathematical analysis. Usually divided into definite integral and indefinite integral. Intuitively speaking, for a given positive real function, the definite integral in the real number interval can be understood as the area value (a definite real value) of the curve trapezoid surrounded by curves, lines and axes on the coordinate plane.
I. Formula derivation
∫sin^2xdx
=∫( 1-cos2x)dx/2
=( 1/2)∫( 1-cos2x)dx
=( 1/2)(x-sin2x/2)+C
=(2x-sin2x)/4+C
So the integral of sinx^2 is (2x-sin2x)/4+C.
Second, integration.
1, integral is a core concept in calculus and mathematical analysis. Usually divided into definite integral and indefinite integral. Intuitively speaking, for a given positive real function, the definite integral in the real number interval can be understood as the area value (a definite real value) of the curve trapezoid surrounded by curves, lines and axes on the coordinate plane.
2. In the process of getting bigger (or smaller) and changing forever, a variable in a function gradually approaches a value and "can never coincide with A" ("can never be equal to A, but it is enough to obtain a high-precision calculation result). The change of this variable is artificially defined as" never approaching and never stopping ",which has its own characteristics.
3. Differentiation is to approximate the value of the curve equation at a certain point with the tangent straight line equation, and not specifying a certain point is the relationship that all points satisfy; Integral is divided into definite integral and indefinite integral, and definite integral is to find the area between curve and X axis. The indefinite integral is the equation satisfied by this area.
Two principles of parts integration
1, relatively speaking, whoever is easy to lag behind the differential will get together;
2. The points after exchanging positions are easy to find.
Empirical order: positive, negative, power, third, reference.
For example, if the integrand has an exponential function, the exponent should be put behind the differential, if not, the trigonometric function should be put behind, and the power function should be considered. It should be noted that the order of experience is not absolute, but a general order, and it is more important to master two principles.