Integral of ∫sin(ax^2)cos(ax^2)dx using the Power Series

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In this video, we simplify find the integral of sin(ax^2)cos(ax^2)dx by first simplifying the expression to (1/2)sin(2ax^2). Then the integral of sin(2ax^2) is a fresnel integral that doesn't have a solution that can be expressed in terms of elementary functions.

However, we can find an analytical solution in terms of the infinite sum of the power series for the integral of sin(2ax^2).

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  1. MasterWuMathematics
  2. Augustin-Jean Fresnel (Academic)
  3. Physics (Field Of Study)
  4. Power Series
  5. Tayloer Series
  6. Mathematics
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