Posted by Ben on Tuesday, December 4, 2007 at 11:04pm.
Find the indefinite integral of
3 sin x - 3 cos x.
It is -3 sin x - 3 cos x.
Finally, evaluate that at x = pi and subtract the value at x = 0, the two limts of integration.
I get (0 + 3) - (0 -3(1)) = 6
Over part of the interval, the 3 cos x curve is higher than 3 sin x. That part of the area integral is counted as negative
As drwls noted, the cosine curve is above the sine curve from x =0 to x=pi/4 and from pi/4 to pi, the sine curve is higher.
So the calculation has to be done in two parts
Area = integral(3cosx - 3sinx)dx from 0 to pi/4 + integral(3sinx - 3cosx)dx from pi/4 to pi.
I got 6√2 as a final answer
Related Questions
calc - find the area between the x-axis and the graph of hte given function over...
Math - 1. Find y'(x) when xsecy - 3y sinx = 1 a) (3ycosx - sec y) / (xsec^2y...
Calculus - These are the two problems from my homework I don't get.. can you...
trig - Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=0
trig - Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=0
Math - Use the definite integral to find the area between the x-axis over the ...
calculus - Use left endpoints and 9 rectangles to find the approximation of the ...
math - find the area between the x-axis and the graph of hte given function over...
calculus - A particle is moving along the x- axis so that its velocity at any ...
Calculus - Suppose that the region between the x-axis and the curve y=e^-x for x...
For Further Reading
