(a) Express $\int _ { 0 } ^ { x } \frac { \sin \left( t ^ { 2 } \right) } { t ^ { 2 } } d t$ as a Maclaurin series.(b) Evaluate $\int _ { 0 } ^ { 03 } \frac { \sin \left( x ^ { 2 } \right) } { x ^ { 2 } } d x$ as a series.

Question

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The Answer of (a) Express $\int _ { 0 } ^ { x } \frac { \sin \left( t ^ { 2 } \right) } { t ^ { 2 } } d t$ as a Maclaurin series.(b) Evaluate $\int _ { 0 } ^ { 03 } \frac { \sin \left( x ^ { 2 } \right) } { x ^ { 2 } } d x$ as a series.

(A) Express ∫0xsin⁡(t2)t2dt\int _ { 0 } ^ { x } \frac { \sin \left( t ^ { 2 } \right) } { t ^ { 2 } } d t∫0x​t2sin(t2)​dt

(A) Express $\int _ { 0 } ^ { x } \frac { \sin \left( t ^ { 2 } \right) } { t ^ { 2 } } d t$