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Find \(\displaystyle \int^{1}_{-1} \sin\left(\dfrac{e^x - e^{-x}}{2}\right)\; dx\)

Substituting u = -x yields something similar. What should I do?

 Jun 24, 2019

Best Answer 

 #1
avatar+28130 
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Notice that the integrand is an odd function i.e. if f(x) = sin(sinh(x)) then f(-x) = -f(x).  This means the integral of f(x) from -1 to +1 is zero. 

 Jun 24, 2019
 #1
avatar+28130 
+5
Best Answer

Notice that the integrand is an odd function i.e. if f(x) = sin(sinh(x)) then f(-x) = -f(x).  This means the integral of f(x) from -1 to +1 is zero. 

Alan Jun 24, 2019

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