With a programmable calculator (or a computer), it is possible to evaluate the e

Question

With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of n, using looping. (On a TI use the Is> command or a For-EndFor loop, on a Casio use Isz, on an HP or in BASIC use a FOR-NEXT loop.) Compute the sum of the areas of approximating rectangles using equal subintervals and right end points for n = 10, 30, 50, and 100. (Round your answers to four decimal places.) The region under y = 5 cos x from 0 to ?/2

Explanation / Answer

deltax =0.15708
number of intervals 10
Right Riemann sum =5.85311
deltax =0.15708
Multiply sum by deltax, sum = 0.9194

--------------------------------------
deltax =0.05236
number of intervals 30
Right Riemann sum =18.59425
deltax =0.05236
Multiply sum by deltax sum = 0.9736

-----------------------------------
deltax =0.03142
number of intervals 50
Right Riemann sum =31.3284
deltax =0.03142
Multiply sum by deltax sum = 0.9842
--------------------------------------...
deltax =0.01571
number of intervals 100
Right Riemann sum =63.16072
deltax =0.01571
Multiply sum by deltax = 0.9921
--------------------

Note:
Actual integration gives:
Integral of cos x = sin x from 0 to PI/2
= sin(PI/2) - sin(0) = 1-0 = 1

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.