# Math

Find the area between y=3sinx and y=3cosx over the interval [0,pi].

1. 👍 0
2. 👎 0
3. 👁 207
1. 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

1. 👍 0
2. 👎 0
posted by drwls
2. 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

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### trig

Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=0

asked by Piwokazi on September 12, 2011
2. ### trig

Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=0

asked by Piwokazi on September 12, 2011
3. ### Math

1. Find y'(x) when xsecy - 3y sinx = 1 a) (3ycosx - sec y) / (xsec^2y - 3sinx) b) (3cosx - sec x) / (xsecytany - 3sinx) c) (3ycosx - sec y) / (xsecytany - 3sinx) d) (3ycosx - secytany) / xsec^2y - 3sinx) This is what I did: xsecy

asked by Donna on May 19, 2008
4. ### Pre-Calculus

Solve the equation on the interval [0,2pi). 2sin^2x-3sinx+1=0 (2sinx+1)(sinx+1) I don't think I did the factoring correctly. When I multiply it out to double check I get 2sin^2x+3sinx+1

asked by Jan on October 27, 2017
5. ### Precalculus

2sin^2x+3cosx=3 find all solutions in the interval [0,2pi]

asked by Megan on December 8, 2010
6. ### Calculus

f(x, y) = 3ycos x, 0 ≤ x ≤ 2π Finding the locla minima, maxima, and saddle points. Having difficulty as so far I have: Fx = -3ysinx Fy = 3cosx Fxx = -3ycosx Fyy = 0 Fxy = -3sinx I have set both Fx and Fy equal to 0 but am not

asked by OscarEE on October 19, 2016
7. ### Math - Solving Trig Equations

Solve each equation for 0 is less than and equal to "x" is less than and equal to 360 3sinx = 2cos^{2}x ----- I don't know how to solve this equation...this is what I have, but I don't know if I'm on the right track or not 3sinx =

asked by Anonymous on November 21, 2007
8. ### Calculus

Consider the function f(x)=3cosx−cos^(3)x for 0

asked by Nicola on November 27, 2011