To determine

To evaluate:

∫01u+2u-3 du

Answer

∫01u+2u-3 du= -376

Explanation

1) Concept:

i) The Fundamental Theorem of Calculus (part 2): Suppose  f is continuous on [a, b], then

∫abfxdx=Fb-F(a), where F is antiderivative of  f, that is F'=f.

ii) Separate out the integration and then use antiderivative of each term

2) Calculation:

∫01u+2u-3 du

After simplifying the equation, the above integration becomes

∫01(u2-3u+2u-6) du= ∫01u2-u-6 du

After separating the integration, the above integration becomes

∫01u2 du-∫01u du- ∫016 du

By using the antiderivative of each term,

u3310-u2210-6[u]10

Applying the Fundamental Theorem of Calculus

13-0-12-0-6(1-0)

After simplifying,

13-12-6=-16-6=-376

Conclusion:

Therefore,

∫01u+2u-3 du= -376