Question

estimate the follwoing question by using a power series expansion of sin x with five non-zero terms.

Answer 1

\[\int\limits_{0}^{\pi^2} [ \sin (\sqrt{x})] dx\]

Answer 2

\[\Large

sinx=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}
\]replace x by \[\sqrt{x}\]

Answer 3

\[\Large

sin\sqrt{x}=\sqrt{x}-\frac{\sqrt{x^3}}{3!}+\frac{\sqrt{x^5}}{5!}-\frac{\sqrt{x^7}}{7!}+\frac{\sqrt{x^9}}{9!}\]

Answer 4

\[\Large \int\limits_{0}^{\pi^2}\Large

(\sqrt{x}-\frac{\sqrt{x^3}}{3!}+\frac{\sqrt{x^5}}{5!}-\frac{\sqrt{x^7}}{7!}+\frac{\sqrt{x^9}}{9!} )dx\]

Answer 5

the rest is yours (:

Answer 6

that makes so much more sense now, thank you! i learned this information within hours so ive been stuck haha