By trapezoidal rule, the approximate value of the integral ₀^6 d x 1+x^2 is

Step-by-step solution

Given that, I= ₀^6 d x 1+x^2 ....(i) From Eq. (i), f(x)= 1 1+x^2 Now, divide the interval [0,6] into six parts each of width h= 6-0 6 =1 The value of f(x) are given below array c|c|c|c|c|c|c|c x & 0 & 1 & 2 & 3 & 4 & 5 & 6 f(x) & 1 & 0.5 & 0.2 & 0.1 & 0.0588 & 0.0385 & 0.027 array The trapezoidal rule is aligned _ x₀ ^ x₀+n h y d x= & h 2 [ (y₀+y_n ) . & .+2 (y₁+y₂+y₃+ +y_ n-1 ) ] aligned aligned ₀^6 1 1+x^2 d x & = 1 2 [(1+0.027)+2 0.5+0.2 & +0.1+0.0588+0.0385 ] & = 1 2 [1.027+2(0.8973)] & = 1 2 [1.027+1.7946] & =