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Math Help - Find the area between two trig functions

  1. #1
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    Find the area between two trig functions

    Region R is enclosed by the graphs of y=tanx^2, y=(1/2)secx^2. Find R. Take it from [0,1]

    For the integral I got (1/2)tanx-tanx-x.
    Taking the integral from [0,1] I got about .22129. Is that right?
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  2. #2
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    Quote Originally Posted by ment2byours View Post
    Region R is enclosed by the graphs of y=tanx^2, y=(1/2)secx^2. Find R. Take it from [0,1]

    For the integral I got (1/2)tanx-tanx-x.
    Taking the integral from [0,1] I got about .22129. Is that right?
    you are aware that the curves intersect at \frac{\pi}{4} , right?

    A = \int_0^{\frac{\pi}{4}} \frac{\sec^2{x}}{2} - \tan^2{x} \, dx + \int_{\frac{\pi}{4}}^1 \tan^2{x} - \frac{\sec^2{x}}{2} \, dx

    A = .3495
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