Let R be the region enclosed by the graph of y=sin e^x^2, the x-axis, and the lines x=-1 and x=1. What's the closest integer approximation of the area of R?

Answer: 2

Since it's x-axis, don't you set up a integral with dx at the end? How do I take that integral? Show your work.

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area = 2){0, 1}sin(e^x^2)) dx = 1.772 ~ 2 (calculated by TI-84)

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Estimation without using a graphing calculator:

f(x) = sin(e^x^2))

f'(x) = cos(e^x^2))e^(x^2) (2x) on [0, 1]

Solve f'(x) = 0 for x,e^x^2 = pi/2

x = sqrt[ln(pi/2)]

So, fmin = f(0) = sin(1), and fmax = f(sqrt[ln(pi/2)]) = sin(pi/2) = 1

2sin(1) < 2){0, 1}sin(e^x^2)) dx < 2*1

1.683 < 2){0, 1}sin(e^x^2)) dx < 2

Answer: 2

Richard P. | Fairfax County Tutor for HS Math and ScienceFairfax County Tutor for HS Math and Sci...

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