Polynomials: Integration

Worked Solution

Integrating Powers:

a tn dt =

a tn+1 n + 1

+ constant

Integrating Sums:

(A + B) dt =

A dt +

B dt

5 t3 dt =

5 4

t4 + g

–t2 dt =

–  1 3

t3 + f

–3 t dt =

–  3 2

t2 + e

–4 dt =

–4

t + d

All the constants are arbitrary so when we sum these, we replace them by a single constant, for example c

(5 t3 – t2 – 3 t – 4) dt =

5 4 t4 –  1 3 t3 –  3 2 t2 – 4 t

+ c