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How do you find the definite integral of #13e^-(cos(x)) sin(x) dx# from #[ 0 , pi/2]#?

Answer 1

Samantha Adkison

#int_0^(pi/2) 13*e^-cos x *sin x # # dx=8.21757#

#int_0^(pi/2) 13*e^-cos x *sin x # # dx #

#int 13 e^-cos x * sin x# #dx#= #13 e^-cos x#

Evaluating the integral from #0# to #pi/2#

#=13[e^-cos (pi/2) - e^-cos 0]#

#=13[e^0 - e^-1]#

#=13[1-e^-1]#

#8.21757#

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Answer 2

Axel Alvarez

To find the definite integral of (13e^{-\cos(x)} \sin(x)) from (0) to (\frac{\pi}{2}), you integrate the function over the given interval and then evaluate it at the upper and lower limits of integration.

[ \int_{0}^{\frac{\pi}{2}} 13e^{-\cos(x)} \sin(x) , dx ]

Unfortunately, this integral doesn't have a simple antiderivative that can be expressed in terms of elementary functions. Therefore, you might need to use numerical methods to approximate the value of this integral.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.