Problem 32 Hard Difficulty

Use a power series to approximate the definite integral to six decimal places.
$ \int^{0.3}_0 \frac {x^2}{1 + x^4} dx $

Answer

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Video Transcript

The problem is, here's our power. Siri's to approximate the definite integral to sixty two more places integral from zero to zero point three Ex squire over one US X to the power for the X. So first to have one over one plus X. This is a call to some of their own community. Next, you want the part ofthe end times thanks to the problem on Behalf X squire over one class next to the power off or this is called Black Square Tams. So we use this identities just to replace Max. I ax to the part ofthe war. So we have. This is integral. This is X squared times, some from zero to infinity. I think you want the power and Sam's ex to the power off Warren, which is a call to some from zero to infinity. Make one arms Jax to the party off or us too the integral from zero to zero point three exploiter or a long class next to the horrible or yes, this is the one true some from Cyril Team unity, selective once a part of and arms Act two, The part dwarf or class three over one past three from zero to zero point three things to what end? You see country three this term. So we have there a point to read to the power off. Fifteen is about one point three halves. Tend to negative Pete. So go have this's apart. Zero point three two power off three over three, minus zero point three to the power off selling over seven US zero point three to the part ofthe eleven over Calvin, which is about zero point zero zero it nine six nine.