(a) Express the indefinite integral ∫ sin ( x 2 ) d x {\displaystyle \int \sin(x^{2})~dx} as a power series.
(b) Express the definite integral ∫ 0 1 sin ( x 2 ) d x {\displaystyle \int _{0}^{1}\sin(x^{2})~dx} as a number series.
Solution:
(a)
(b)
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as a power series.
as a number series.