To evaluate: ∫01(1-8v3+16v7)dv
i) The Fundamental Theorem of Calculus (part 2)
ii) Separate out the integration and then use antiderivative of each term
The Fundamental Theorem of Calculus: Suppose f is continuous on [a, b], then
∫abfxdx=Fb-F(a), where F is antiderivative of f, that is F'=f.
∫01(1-8v3+16v7)dv By separating the integral
By using the antiderivative of each term,
Applying the Fundamental Theorem of Calculus