The intensity of light with wavelength $\lambda$ traveling through a diffraction grating with $N$ slits at an angle $\theta$ is given by $$I(\theta)=\frac{N^2 \sin^2(k)}{k^2},$$ where $k=(\pi N d \sin(\theta))/\lambda$ and $d$ is the distance between adjacent slits. A helium-neon laser with wavelength $\lambda=632.8 \times 10^{-9}$ meters is emitting a narrow band of light, given by $-10^{-6} < \theta < 10^{-6},$ through a grating with 10,000 slits spaced $10^{-4}$ meters apart. Use the Midpoint Rule with $n$ = 10 to estimate the total light intensity $$\int_{-10^{-6}}^{\,10^{-6}} {I(\theta)}\, d\theta$$ emerging from the grating.

Note: Make sure your answer is correct to four decimal places.

Total light intensity $\approx$