Q4. Consider the integral 4 1 = ₁² (x + 1)(x + 5) dx (a) Evaluate the integral analytically. (b) Evaluate the integral numerically by using Gaussian quadrature with n=2 nodes where Gaussian quadrature nodes, Zi Weight factors, Wi W₁ = W₂ = 1 Z₁ = -0.57735, Z₂ = 0.57735 b-a Hint: x = a + 2+ (z+1) changes the interval [a,b] to [-1,1] where a ≤ x ≤ b and -1 ≤ z ≤ 1. Q5. Use Newton's iteration to approximate the value √7 in the interval [1,2]. Start the iteration with x = 1 and perform the first 4 iterations. Use 4-digit chopping in your computations. Hint: Define a function f(x)=x²-7.