Area bounded by e^sinx, x-axis, x = -2, and x = 3

[tarynt1]

Find the area bounded by f(x) = e^sinx, the x-axis and the lines x = -2 and x = 3. Show the integral that supports your answer.

I'm having trouble taking the anti-derivative of (e^sinx)dx because we haven't dealt with that in class. I'm coming up with (e^sinx) / cosx. I'm also ending up with a negative area . . . -0.195.

 

[galactus]

I don't think it is integrable by elementary means. You could try a Riemann sum. I used midpoint and 20 partitions on this graph.
The actual area is 7.09258626232.

That's fairly close. Of course, the more partitions, the more accurate.