Calculate the integral of (x^3-4x^2+1) from 1 to 2 using the fundamental theorem of calculus.
Fundamental theorem of calculus says:
Let `f` be continous real-valued function defined on segment `[a,b]` and let `F` be defined as
Then `F` is continous and differentiable on `(a,b)` and for all `x in (a,b)`
For calculating definite integral we usually use corollary of this theorem, also known as Newton-Leibniz formula
Same assumptions as in previous theorem and
This is sometimes called second fundamental theorem of calculus.
Now to calculate your integral:
`int_1^2(x^3-4x^2+1)dx=` by linearity of integral
Also see the link below.