Calc 2: Area under the curve

Find the area of the region enclosed between y=2sin(x and y=3cos(x) from x=0 to x=0.4pi

Hint: Notice that this region consists of two parts.

Notice: I'm getting 1.73762 but apparently that is wrong.

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  1. Find x where 2sin(x)=3cos(x) (div by cos)
    2tan(x)=3
    tan(x)=1.5
    x=56.31degr
    Area(from x=0 to x=56.31)=
    (3sin(56.31)+2cos(56.31)-(3sin(0)+2cos(0))
    =3.60555-2=1.60555
    Area(from x=56.31 to x=72)=
    (-2cos(72)-3sin(72))-(-2cos(56.31)-3sin(56.31))=-3.47120-(-3.60555)=0.13435
    The total area=1.60555+0.13435=1.7399

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