The trapezoidal approximation of ∫ sin x dx from 0 to pi using 4 equal subdivisions of the interval of integration is a) pi/2 b) pi c) (pi/4)(1+sqrt(2)) d) (pi/2)(1+sqrt(2)) e) (pi/4)(2+sqrt(2)) Answer: C Please show all your work. 4/19/2014 | Sun from Los Angeles, CA | 1 Answer | 0 Votes Mark favorite Subscribe Comment
The trapezoidal approximation for the definite integral of f(x) between the points a and b is: T_{n} = [(b-a)/2n][f(x_{0})+2f(x_{1})+2f(x_{2})+2f(x_{3})+...+f(x_{n})] Where a and b are the limits of the integration and n = the number of trapezoids used in the estimate. In your case: f(x)= sinx a=x_{0}=0, b=x_{n}=pi, n=4 T_{4} = (pi/8)[sin(0)+2sin(pi/4)+2sin(pi/2)+2sin(3pi/2)+sin(pi)] Solve for T_{4} 4/20/2014 | Philip P. Comment