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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
 
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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