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    I need to find the area between r^2 = sin(2theta) and r^2= cos(2theta)...I graphed them, but I'm not sure about the intervals...I tried pi/4 and 0 and then multiplied the answer by two, but it didn't work. So how will I know the intervals? Do I just find the point of intersection?

    Thank you in advance
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    I hope I can describe this OK.

    The two graphs are like double-loops, at an angle of 45 degrees to each other. Centred on the origin.

    There are two areas of overlap. One in the1st quadrant and one in the 3rd quadrant.

    Draw a line y = mx through the intersection points. This line will bisect each of the two areas of overlap.

    Now find the area under the curve r^2=cos*2t in the 1st quadrant. Also find the area under the same curve from t = 0 to t = atan(m).

    Subtract these areas.

    Multiply by 4.
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    (Original post by steve10)
    I hope I can describe this OK.

    The two graphs are like double-loops, at an angle of 45 degrees to each other. Centred on the origin.

    There are two areas of overlap. One in the1st quadrant and one in the 3rd quadrant.

    Draw a line y = mx through the intersection points. This line will bisect each of the two areas of overlap.

    Now find the area under the curve r^2=cos*2t in the 1st quadrant. Also find the area under the same curve from t = 0 to t = atan(m).

    Subtract these areas.

    Multiply by 4.
    Shouldn't it be from theta=0 to theta=pi/4 ?
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    The 1st area I mentioned, under the curve r^2=cos*2t in the 1st quadrant, is from theta = 0 to pi/4.

    The 2nd area is from 0 to atan(m), where m is the slope of the bisecting line. You have to figure out m yourself from the intersection of the two curves.
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    Lol this is my day job
 
 
 
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