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^2x-3cosx+sinxcosx-3sinx=0
- trig - Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=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 x-axis over the ...
- math - find the area between the x-axis and the graph of the given function over...
- calculus - Find the area between the graph of f and the x-axis 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 x-axis over the ...

More Related Questions