## University Calculus: Early Transcendentals (3rd Edition)

$$| Error| \lt 0.00011$$
We integrate the integral with respect to $x$ taking a lower limit as $0$ and upper limit as $1$. $\int_0^{1} \cos t^2 dt=\int_0^{1} [1-\dfrac{t^2}{2}+\dfrac{t^{8}}{4 !}-...] dx$ or, $=[t-\dfrac{t^5}{10}+\dfrac{t^{9}}{9 \cdot 4 !}-...]_0^{10} ....$ So, the error can be calculated as: $| Error| \lt \dfrac{1}{13 \cdot 6 !} \approx 0.00011$