Question

What is the value of the following integral and how are you able to tell from its graph:

the interval of integration is 0 to pi/2
and the integrand is cos^8x dx

Answer 1

I don't see how you can get the exact value from the graph
you could try to estimate it, but no method is prescribed...

Answer 2

Well the entire problem states that four students disagree on the value of the integral... Jack- pi \[\approx 3.14\] Joan- 35 pi/256 \[\approx 0.43\] Ed- 2pi/9-1 \[\approx -0.30\] and Lesley for pi/4 \[\approx 0.79\] ...and then it says use the graph to determine who is right and be able to explain why all the others are wrong. I just don't understand how to determine that

Answer 3

and this is all talking about the same integral I sent earlier

Answer 4

well let's look at the graphthis is (more or less) the shape of the graph, right?
I would try to approximate this with a triangle I guess

Answer 5

\[\frac12(1\cdot\frac\pi2)=\frac\pi4\]so I guess I like Lesley's answer