Question

How do you evaluate `int sin(x^2)dx` from -1 to 2?

Answer 1

I = 1.084

Explanation:

If you wrote the problem correctly, the answer
involves Fresnel Integrals and that is Graduate Level
Math for a Math Major.

I suspect you meant to write

`I = int (sin x)^2 dx , x = -1, 2`
`I = 1/2 [ x - sin x cos x ] + C`

For x = 2 radians
`I = 1/2 [ 2 - sin 2 cos 2 ] = 1/2 [ 2 - ( 0.909 ) ( - 0.416 ) ]`
`I = .811`

For x = - 1 radian
`I = 1/2 [ -1 - sin (-1) cos (-1) ] = 1/2 [ -1 - ( -0.84 ) ( 0.54 ) ]`
`I = - 0.273`
`I = 0.811 - ( - 0.273 ) = 1.084`