Integrals -zambak- [repack]

| Differentiation Rule | Integration Rule (Formula) | |----------------------|----------------------------| | ( \fracddx(x^n) = n x^n-1 ) | ( \int x^n , dx = \fracx^n+1n+1 + C \ (n \neq -1) ) | | ( \fracddx(e^x) = e^x ) | ( \int e^x , dx = e^x + C ) | | ( \fracddx(\ln|x|) = \frac1x ) | ( \int \frac1x , dx = \ln|x| + C ) | | ( \fracddx(\sin x) = \cos x ) | ( \int \cos x , dx = \sin x + C ) | | ( \fracddx(\cos x) = -\sin x ) | ( \int \sin x , dx = -\cos x + C ) | | ( \fracddx(\tan x) = \sec^2 x ) | ( \int \sec^2 x , dx = \tan x + C ) |

: Focuses heavily on calculating the area under a curve, area between curves, and real-world geometric modeling. 2. Indefinite Integrals and the Antiderivative Integrals -Zambak-

Decompose ( \fracP(x)Q(x) ) into simpler fractions when ( Q(x) ) factors. | Differentiation Rule | Integration Rule (Formula) |

Finding the area between curves and the x-axis or between two different functions. Finding the area between curves and the x-axis

An integral is a mathematical operation that finds the area under a curve or the accumulation of a quantity over a defined interval. It is denoted by the symbol ∫. Integrals are used to solve problems in physics, engineering, economics, and other fields.

f(c)=1b−a∫abf(x)dxf of c equals the fraction with numerator 1 and denominator b minus a end-fraction integral from a to b of f of x space d x Advanced Functions (Special Sections)

Always look for the "inside" function whose derivative matches another part of the integrand. 2. Integration by Parts