1.Solve the differential equation $\frac{dy}{dx} + y = e^{-x}$ with initial condition $y(0) = 1$.
2.Evaluate the Gaussian integral $\int_{-\infty}^{\infty} e^{-x^2} dx$.
3.Find the area bounded by the curve $y = \sin x$ and the x-axis from $x = 0$ to $x = 2\pi$.
4.A particle moves along a curve $r(\theta) = a(1 + \cos\theta)$. Find radial and transverse components of velocity.
