# Math Help - Finding area under graph by integration

1. ## Finding area under graph by integration

Find the exact value of the area of the region enclosed between the x−axis and the
graph of the function f(x) = 2 sin x + 2√3 cos x on the interval [0,π].
HINT: It might be helpful to first write f in the form f(x) = Asin(x+K) for appropriate
constants A and K.

K=phase
A=amplitude

2. $f(x)=4\sin \left( x+\frac{\pi }{3} \right),$ so the expected area is given by $\int_{0}^{\frac{2}{3}\pi }{4\sin \left( x+\frac{\pi }{3} \right)\,dx}-\int_{\frac{2}{3}\pi }^{\pi }{4\sin \left( x+\frac{\pi }{3} \right)}\,dx.$