Explanation Given: The given function of this question is f ( x ) = sin ( m x ) sin ( n x ) The graph: The graph was obtained as follows. Conjecture for I = 0 is For any m ≠ n ; I = ∫ 0 π f ( x ) d x = 0 Formula used : The multiplication of sin A and sin B is given by, sin A sin B = 1 2 [ cos ( A − B ) − cos ( A + B ) ] Interpretation: When we are calculating I = ∫ 0 π f ( x ) d x using a graph, we measure the area under the curve of f ( x ) . In this graph we have two curves of f ( x ) with different values for m and n . First, we consider the curve for m = 2 and n = 4 . There we can see two peaks above the x axis and two valleys lower the x axis. To measure the area under the curve we can get the width and the heights of these peaks and valleys. The widths are nearly two-two and half squares of these four shapes. And the heights are also equal to about three squares. Therefore we can say that the area under the curve f ( x ) = sin ( 2 x ) sin ( 4 x ) is approximately zero because the summation of same areas in opposite values...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 5, Problem 81CRE

To determine

To plot:

The graph of $f (x) = \sin (m x) \sin (n x)$ on $[0, π]$ for the pair $(m, n) = (2, 4), (3, 5)$

Theapproximate value ofeach $I = \int_{0}^{π} f (x) d x$ and a conjecture for when $I = 0$ using the plot.

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Chapter 5, Problem 80CRE

Chapter 5, Problem 82CRE

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Chapter 5 Solutions

Calculus - Standalone book

Ch. 5.1 - Prob. 1PQ Ch. 5.1 - Prob. 2PQ Ch. 5.1 - Prob. 3PQ Ch. 5.1 - Prob. 4PQ Ch. 5.1 - Prob. 5PQ Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - 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To plot: The graph of f ( x ) = sin ( m x ) sin ( n x ) on [ 0 , π ] for the pair ( m , n ) = ( 2 , 4 ) , ( 3 , 5 ) Theapproximate value ofeach I = ∫ 0 π f ( x ) d x and a conjecture for when I = 0 using the plot.

Solution Summary: The author plots the graph of f (x) = sin (m x ) and a conjecture for when I = 0 using the plot.

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To plot:

The graph of $f (x) = \sin (m x) \sin (n x)$ on $[0, π]$ for the pair $(m, n) = (2, 4), (3, 5)$

Theapproximate value ofeach $I = \int_{0}^{π} f (x) d x$ and a conjecture for when $I = 0$ using the plot.

Want to see the full answer?

Chapter 5 Solutions

To plot: The graph of f ( x ) = sin ( m x ) sin ( n x ) on [ 0 , π ] for the pair ( m , n ) = ( 2 , 4 ) , ( 3 , 5 ) Theapproximate value ofeach I = ∫ 0 π f ( x ) d x and a conjecture for when I = 0 using the plot.

Solution Summary: The author plots the graph of f (x) = sin (m x ) and a conjecture for when I = 0 using the plot.

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To plot: The graph of f(x)=sin(mx)sin(nx)on [0,π] for the pair (m,n)=(2,4),(3,5) Theapproximate value ofeach I=∫0πf(x)dx and a conjecture for when I=0using the plot.

Want to see the full answer?

Chapter 5 Solutions

To plot:

The graph of $f (x) = \sin (m x) \sin (n x)$ on $[0, π]$ for the pair $(m, n) = (2, 4), (3, 5)$

Theapproximate value ofeach $I = \int_{0}^{π} f (x) d x$ and a conjecture for when $I = 0$ using the plot.