Explanation Given data: y The given integral is ∫ -π/4 π/4 sec 2 x d x Formula used: ∫ sec 2 x d x = tan x + C , Calculation: The given integral is F = ∫ -π/4 π/4 sec 2 x d x ⇒ F = ∫ -π/4 π/4 sec 2 x d x x = [ tan x ] -π/4 π/4 = ( tan π 4 -tan ( - π 4 ) ) =2tan π 4 = 2 × 1 = 2 Thus, the value of integral that calculates area between the curve of integrand and the x -axis is 2.0. Now, the graph of the function on the interval [ -π/4,π/4 ] shown in figure here

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 4, Problem 32SC

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To find: The exact value of given integral and sketch the area described by the definite integral and verify the reasonability of value of integral.

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Chapter 4, Problem 31SC

Chapter 4, Problem 33SC

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1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .

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The exact value of given integral and sketch the area described by the definite integral and verify the reasonability of value of integral.

Solution Summary: The author explains that the exact value of integral is 2.0 that is equal to the calculated area 2.09. The curve is symmetrical about y-axis.

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To find: The exact value of given integral and sketch the area described by the definite integral and verify the reasonability of value of integral.

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