Tim T. answered • 05/03/20

Math: K-12th grade to Advanced Calc, Ring Theory, Cryptography

Greetings! Lets solve this shall we ?

So, we must find the approximate area of the curve f(x) = 2x^{3} - 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(x_{0}) + 2f(x_{1}) + 2(x_{2}) + 2f(x_{3}) + f(x_{4})], 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 ≈ T_{4} = (6/2)[ f(5) + 2f(11) + 2f(17) + 2f(23) + f(29)] .......After evaluating the function at each interval, we finally get

**A ≈ T**_{4}** = 3[250+2(2656)+2(9814)+2(24316)+48754] = 367728 units**

I hope this helped!