We learned Euler's method today there is one hw problem totally stunned my hat off. It says: Use Euler's method to approximate ∫ 0 2 e − u 2 d u. I know Euler's method is y n + 1 = y n + h f ( t n , y n ), but this is for y ′ right? somehow I can compute an integral? This is supposed to be done using computer, I know how to use Euler's method to solve equation like y ′ = 2 y − 3 e − t .

Question

We learned Euler&#039;s method today there is one hw problem totally stunned my hat off. It says: Use Euler&#039;s method to approximate       ∫    0    2        e          −              u        2              d  u. I know Euler&#039;s method is       y          n      +      1        =      y    n    +  h  f  (      t    n    ,      y    n    ), but this is for       y    ′   right? somehow I can compute an integral? This is supposed to be done using computer, I know how to use Euler&#039;s method to solve equation like       y    ′    =  2  y  −  3      e          −      t      .

pulpasqsltl · Accepted Answer

Let   y  (  t  )  =      ∫    0    t        e          −              u        2              d  u. By the fundamental theorem of calculus, y satisfies the differential equation      y    ′    =      e          −              t        2            You are trying to approximate   y  (  2  ). So it is the sort of problem you know how to solve.

Hailee Stout · Accepted Answer

Try to solve this system:      y    ′    =      e          −              x        2            Start at point 0 and march towards 2.

We learned Euler's method today there is one hw problem totally stunned my hat off. It says: Use Eul

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