   Chapter 8.5, Problem 58E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Meteorology The average monthly precipitation P (in inches) for Lake City, Minnesota, can be modeled by P = 1.91     sin ( 0.55 t − 2.22 ) + 2.74 ,     0 ≤ t ≤ 12 where t is the time (in months), with t = 1 corresponding to January. Find the total annual precipitation for Lake City. (Source: National Climatic Data Center)

To determine

To calculate: The total annual precipitation for Lake city, when average monthly precipitation P in inches is given as P=1.91sin(0.55t2.22)+2.74 for 0t12.

Explanation

Given Information:

The average monthly precipitation P in inches is given as P=1.91sin(0.55t2.22)+2.74 for 0t12.

Formula used:

The formula for definite integral of absinnudu.

absinnudu=[cosnun]ab

The formula for integral of abdu.

abdu=[u]ab

Calculation:

Consider the average monthly precipitation for Lake city.

P=1.91sin(0.55t2.22)+2.74

The total annual precipitation for Lake city is calculated by integrating the average monthly precipitation for Lake city for t=0 to t=12, which can be mathematically written as:

012Pdt=012[1.91sin(0.55t2.22)+2.74]dt

Rewrite.

012Pdt=0121.91sin(0.55t2.22)dt+0122.74dt=1

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