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Chapter 5: Q. 60 (page 493)

Prove that the trapezoid sum is equivalent to the average of the left and right sums:TRAP(n)=LEFT(n)+RIGHT(n)2

Short Answer

Expert verified

The required equation is proved.

Step by step solution

01

Step 1. Given Information

The given data is the trapezoid sum is equivalent to the average of the left and right sums.

02

Step 2. Explanation

The left sum and right sum are expressed as LEFT(n)=鈭�K=1nf(xk-1)鈭�xandRIGHT(n)=鈭�K=1nf(xk)鈭�x

Substitute the approximation of left and right sum in the right hand side of,

localid="1649659751078" LEFT(n)+RIGHT(n)2=鈭�K=1nf(xk-1)鈭�x+鈭�K=1nf(xk)鈭�x2=鈭�K=1nf(xk)+f(xk-1)2鈭�x=TRAP(n)

The right hand side of the equation is the trapezoid sum.

Hence, it is proved.

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