Hello all, I am new to these forums. Please let me know if I am off base a bit.
I am unsure of how to even start the following problem, so holding my hand would be appreciated.
Let \(\displaystyle A\, =\, \displaystyle{ \int_0^1 \, } e^{-t^2}\, dt\) and \(\displaystyle B\, =\, \displaystyle{ \int_0^{\frac{1}{2}} \,} e^{-t^2}\, dt.\) Evaluate the iterated integral:
. . . . .\(\displaystyle I\, =\, 2\, \displaystyle{ \int_{-\frac{1}{2}}^1 \, }\) \(\displaystyle \left[\displaystyle{ \int_0^x \,} \exp\left(-y^2\right)\, dy \right]\, dx\)
in terms of \(\displaystyle A\) and \(\displaystyle B.\) These are positive integers \(\displaystyle m\) and \(\displaystyle n\) such that:
. . . . .\(\displaystyle I\, =\, mA\, -\, nB\, +\, e^{-1}\, -\, e^{-\dfrac{1}{4}}\)
Use this fact to check your answer.
Thank you in advance.
I am unsure of how to even start the following problem, so holding my hand would be appreciated.
Let \(\displaystyle A\, =\, \displaystyle{ \int_0^1 \, } e^{-t^2}\, dt\) and \(\displaystyle B\, =\, \displaystyle{ \int_0^{\frac{1}{2}} \,} e^{-t^2}\, dt.\) Evaluate the iterated integral:
. . . . .\(\displaystyle I\, =\, 2\, \displaystyle{ \int_{-\frac{1}{2}}^1 \, }\) \(\displaystyle \left[\displaystyle{ \int_0^x \,} \exp\left(-y^2\right)\, dy \right]\, dx\)
in terms of \(\displaystyle A\) and \(\displaystyle B.\) These are positive integers \(\displaystyle m\) and \(\displaystyle n\) such that:
. . . . .\(\displaystyle I\, =\, mA\, -\, nB\, +\, e^{-1}\, -\, e^{-\dfrac{1}{4}}\)
Use this fact to check your answer.
Thank you in advance.
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