Given the following definite integral and $n = 4,$ answer the following questions. (Round your answers to six decimal places.) $$\int_{0}^{1} \!\sin(x^2)\, dx$$

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1. Use the Trapezoidal Rule to approximate the definite integral.
Answer: $T_4 =$

2. Use the Midpoint Rule to approximate the definite integral.
Answer: $M_4 =$

3. Use Simpson's Rule to approximate the definite integral.
Answer: $S_4 =$

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