Evaluate Definite Integral Using Trapezium Rule: 4, 8 & 16 Subs

[escobar147]

∫cos x + sin x

lower limit: 0 upper limit: pi

correct answer: 4 intervals: 1.8962, 8 intervals: 1.9742, 16 intervals: 1.9936

i cannot seem to get the correct answer, here is my attempt:

x values cosx + sinx values
0 1
1.042 0.998
2.0944 0.993
3.1415 0.9984

2(0.998 +0.993) + 1 + 0.9984 = 5.9966

h= b-a/n n=4, b-a = pi

h= 0.7853

h/2(5.9966) = 2.3548

this is for the 4 sub interval part of the question and is incorrect... any help would be massively appreciated!

 

[Mark44]

∫cos x + sin x

lower limit: 0 upper limit: pi

correct answer: 4 intervals: 1.8962, 8 intervals: 1.9742, 16 intervals: 1.9936

i cannot seem to get the correct answer, here is my attempt:

x values cosx + sinx values
0 1
1.042 0.998
2.0944 0.993
3.1415 0.9984

You have three subintervals, not four. The endpoints of your subintervals should be at 0, [itex]\pi[/itex]/4, [itex]\pi[/itex]/2, [itex]3\pi[/itex]/4, and [itex]\pi[/itex].

2(0.998 +0.993) + 1 + 0.9984 = 5.9966

h= b-a/n n=4, b-a = pi

h= 0.7853

h/2(5.9966) = 2.3548

this is for the 4 sub interval part of the question and is incorrect... any help would be massively appreciated!

 

[escobar147]

You have three subintervals, not four. The endpoints of your subintervals should be at 0, [itex]\pi[/itex]/4, [itex]\pi[/itex]/2, [itex]3\pi[/itex]/4, and [itex]\pi[/itex].

i believe these are the correct values:
0 1
.785 1.414
1.570 1
2.356 0
3.1415 -1

how are they found? when i plug the x values into cos x + sin x, my answers are different?

 

[HallsofIvy]

Your calculator should be in radian mode, not degrees!

 

[escobar147]

Your calculator should be in radian mode, not degrees!

ah... i see... there's 3 hours i will never get back :)