Use the Trapezoid rule to approximate

Question

Use the Trapezoid Rule to approximate the area under the curve f(x)=2x^3-x+5 from x=5 to x=29. Use 4 trapezoids to find your approximation. 

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the approximate area of the curve f(x) = 2x³ - x + 5 between x = 5 and x = 29 and n = 4 representing the number of trapezoids. Then, the Trapezoidal formula for approximating the Area under the curve is

A ≈ T_n = (Δx/2)[ f(x₀) + 2f(x₁) + 2(x₂) + 2f(x₃) + f(x₄)], where (Δx) is the width of each trapezoid in between such that

Δx = (b-a) / n = (29 - 5) / 4 = 24/4 = 6 units

Now we plug in our intervals and numbers to obtain

A ≈ T₄ = (6/2)[ f(5) + 2f(11) + 2f(17) + 2f(23) + f(29)] .......After evaluating the function at each interval, we finally get

A ≈ T₄ = 3[250+2(2656)+2(9814)+2(24316)+48754] = 367728 units

I hope this helped!