Expert: Paul Klarreich - 8/10/2009

Question
Integral and solution please?
i have been asked to use g'(x)= 1/38(2-3sinx-2sin^2*x)exp(2/3sinx)
and x=0.52 and x=2.61

using above information find the area of bounded by the graph of
y=(2sinx-1)(sinx+2)exp(2/3sinx) and by the x axis. rgion whose area is sought does n't extend to x=0 to the left and x=2pi to the right


can someone help and show the working as well.

Answer
Questioner: jaymin patel
Country: United Kingdom
Category: Calculus
Private: No
Subject: maths
Question: Integral and solution please?
i have been asked to use g'(x)= 1/38(2-3sinx-2sin^2*x)exp(2/3sinx)
and x=0.52 and x=2.61

using above information find the area of bounded by the graph of
y=(2sinx-1)(sinx+2)exp(2/3sinx) and by the x axis. rgion whose area is sought does n't extend to x=0 to the left and x=2pi to the right


can someone help and show the working as well.
..................................................
Using the Integrator:

http://integrals.wolfram.com/index.jsp

You get your integral:

-3 exp^((2 Sin[x])/3) Cos[x]

(Probably you do integration by parts, but I didn't work it out.)
Now apply your boundaries, which appear to be  pi/6 and 5pi/6, which is better than using x=0.52 and x=2.61 ... and by the x axis"

Probably you need a calculator.