Caluculus question!?

Question

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.

Edit: To the person who so politely pointed out what was obviously an accidental spelling error, it is "calculus," not "caluculus."

Answer 1

You want the area bounded by:
f(x) = e^(sinx),
the x-axis (which is y = 0)
x = -2, x = 3.

First off, we need to determine if e^(sinx) crosses the x-axis. If it does, then we need to evaluate this as the sum of two areas.

Let f(x) = 0 to solve for any x-intercepts. Then
e^(sinx) = 0. However, if we change this to exponential form, we have ln(0) = sin(x), which will yield no solution. Therefore, it does not cross the x-axis.

The area bounded by the above is given by:

A = Integral (-2 to 3, e^(sinx))dx

This is a difficult integral to solve, which is why the question doesn't ask you to solve it but only to show it.

Answer 2

Learn how to spell Calculus first...