Question

integrate from 0 to (pi/2) ((1/2)sin1)d theta please help
integrate from 0 to (pi/2) ((1/2)sin1)d theta please help
@Mathematics

Answer 1

is this really
\[\int_0^{\frac{\pi}{2}}\frac{1}{2}\sin(1)d\theta\]???

Answer 2

I got pi/4 sin 1 from Wolfram alpha but I don't know how it got that?

Answer 3

is it really sine of 1?? that is a constant. seems odd

Answer 4

yes sin1

Answer 5

\[\sin(1)\] is just a number. you are integrating a constant from 0 to pi/2

Answer 6

just have a rectangle with base
\[\frac{\pi}{2}\] and height
\[\frac{1}{2}\sin(1)\] so area is
\[\frac{\pi}{2}\times \frac{1}{2}\sin(1)\]

Answer 7

so I just "add" pi and plug pi/2 in?

Answer 8

there is no "adding"
it is base times height. base is pi /2, height is 1/2 sin(1)

Answer 9

if you look at your question it says integrate with respect to theta, but there is no theta there. you just have a constant

Answer 10

why is it different than integrating 1 dx which turns into x then you evaluate x at a and b?
I haven't done integration for a long time.

Answer 11

like
\[\int_0^5 4 dx=5\times 4\]

Answer 12

you could do the same thing and you will get the same answer.

Answer 13

oh, so, using your example, I'd have 4x evaluated at 5 and 0 right?

Answer 14

but it is silly to integrate a constant using anti-derivatives. you are trying to find the area of a rectangle, use base times height

Answer 15

I'll use the rectangle from now on.

Answer 16

yes in my example you could say
the antiderivative of 4 is 4x, plug in 5, get 20, plug in 0, get 0, so answer is 20. but that is a waste of time

Answer 17

a constant is a horizontal line, so you are finding the area of a rectangle. base time height does it. in other words it is the constant times the length of the path

Answer 18

yes! thank you for pointing this out.

Answer 19

yw