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

1 Answer
Jul 31, 2017

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