Final answer:
To evaluate the definite integral ∫(1+5ti+6t³j+3tk)dt from -1 to t, integrate each component separately with respect to t and substitute the upper limit t and subtract the value at the lower limit -1.
Step-by-step explanation:
To evaluate the definite integral ∫(1+5ti+6t³j+3tk)dt from -1 to t, we need to integrate each component separately with respect to t. The integral of 1 with respect to t is t, the integral of 5ti is 2.5t²i, the integral of 6t³j is 1.5t⁴j, and the integral of 3tk is 1.5t²k. After simplifying the coefficients, we substitute the upper limit t and subtract the value at the lower limit -1 to find the definite integral.