integration(y1)

integration

the reverse process of differentiation, often notated as ∫

for polynomials each x^n term is integrated and constants are ignored, then a constant of integration c is added

integrating x^n

∫x^n dx = x^(n+1)/n+1 (dx means to integrate with respect to x)

(not suitable for x^-1)

for kx^n the function is integrated as normal and the result is multiplied by k

remember the constant of integration

definite integration

where a is the lower limit and b is the upper limit of x

finding area between a curve and the x axis

definite integration produces a value which represents the area between the curve and the x axis, above the x axis this will be positive and below it will be negative

to find the area when the line goes above and below split the integral into separate regions either side of the x-intercept

finding definite integral on a calculator

definite integrals on a calculator will usually be notated as such