The Definite Integral

[Nat2663]

Estimate the total area between f(x)=cos⁡(x^3) and the x-axis for 0≤ x ≤ π^1/3. (You will want to use a calculator or such to get a reasonably accurate estimate.)

 

[MarkFL]

If you're just supposed to use technology, then see this:

integral of cos(x^3) for x=0 to pi^(1/3) - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

 

[Nat2663]

Thank you, but it says that answer is incorrect.

 

[MarkFL]

Without knowing how many digits of precision are expected, it's hard to say why that is.

 

[Dr.Peterson]

Looking at the graph, the area they want is the sum of the blue and pink areas, which will require integrating each one separately and taking absolute values. It looks like technology is the way to go; are they perhaps expecting a numerical integration on a calculator?

 

[MarkFL]

Ah, I missed that they're looking for the total area and not simply an approximation for the definite integral. In that case, W|A returns an approximation of:

1.1589775724894

 

[HallsofIvy]

I've always thought of paper and pencil as "technology"- they don't grow on trees!