Concept explainers
The area under the curve by RRAM or LRAM method.
Answer to Problem 32E
The area of this curve is 2.
Explanation of Solution
Given information:
The number of rectangles MRAM always gives the accurate approximation to the true area under the curve than RRAM or LRAM.
The Answer is true, MRAM gives more accurate result. The justification is given as below,
RAM means rectangular approximation method; the name suggests the choice we made when determining the heights of the approximating rectangles, and we evaluated the function at the right-hand endpoint of each subinterval for RRAM, at the left-hand endpoint of each subinterval for RRAM and at the midpoint of each subinterval for MRAM, n indicates the number of subintervals.
But here, on applying the RAM program for this function in calculator to get this numbers in this table. Here n indicates the number of subintervals, it means [a, b] is divided into n equal part.
Actual area of this curve is 2. See all the time MRAM is more close to 2 than RRAM or LRAM.
Conclusion:
The time MRAM is more close to 2 than RRAM or LRAM.
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Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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