Search 80,000+ tutors
Ask a question
0 0

Help me with trapezoidal approximation?

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.
Tutors, please sign in to answer this question.

1 Answer

The trapezoidal approximation for the definite integral of f(x) between the points a and b is:
Tn = [(b-a)/2n][f(x0)+2f(x1)+2f(x2)+2f(x3)+...+f(xn)]
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=x0=0, b=xn=pi, n=4
T4 = (pi/8)[sin(0)+2sin(pi/4)+2sin(pi/2)+2sin(3pi/2)+sin(pi)]
Solve for T4