Mathematica Labs | Denis Shubleka

Subject: Calculus

Topic: Integrals

Task 1

Goal: Use Mathematica to find antiderivatives (i.e. indefinite integrals).

Find the indefinite integral symbol in the Basic Math Assistant palette (Advanced
tab), and try a few examples:

∫((x^81)+Cos[x])\[DifferentialD]x

∫(Sqrt[x+2])\[DifferentialD]x
∫Sec[x]\[DifferentialD]x

Task 2

Goal: Use Mathematica to compute definite integrals.

Find the definite integral symbol in the Basic Math Assistant palette (Advanced tab),
and try a few examples:

(∫_1^4)((x^2)+Log[x])\[DifferentialD]x

(∫_(-1)^2)(E^t)\[DifferentialD]t
(∫_((-π)/4)^(π/2))(Cos[x]-Sin[x])\[DifferentialD]x

We can plot and shade the signed area that represents the last example above:

Plot[Cos[x]-Sin[x],{x,((-π)/4),(π/2)},Filling->Axis]

Is the signed area positive or negative? Does this match with Mathematica’s numerical
computation of the definite integral? Explain.

Related Exercises/Notes:

ap-calc.github.io