Posted by Ben on Tuesday, December 4, 2007 at 11:04pm.
Find the area between y=3sinx and y=3cosx over the interval [0,pi].

Math  drwls, Tuesday, December 4, 2007 at 11:27pm
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

Math  Reiny, Wednesday, December 5, 2007 at 12:10am
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
Answer This Question
Related Questions
 Math  1. Find y'(x) when xsecy  3y sinx = 1 a) (3ycosx  sec y) / (xsec^2y  ...
 trig  Help find the general solution to:sin^2x3cosx+sinxcosx3sinx=0
 trig  Help find the general solution to:sin^2x3cosx+sinxcosx3sinx=0
 Calculus  These are the two problems from my homework I don't get.. can you ...
 Math  Use the definite integral to find the area between the xaxis over the ...
 math  find the area between the xaxis and the graph of the given function over...
 calculus  Find the area between the graph of f and the xaxis over the interval...
 Math  Use the limit process to find the area of the region between the graph of...
 Math  Solving Trig Equations  Solve each equation for 0 is less than and equal...
 math  Consider the area between the curve y=x^2 and the xaxis over the ...
More Related Questions