QUESTION 1 Evaluate the integral. ??³ [(?/?(???))i - (10t²)j + (6t/(1+t²)²)k] dt 8i - 90j + (9/10)k 8i + 90j + (9/10)k 4i - 90j + (27/10)k 8i - 90j + (27/10)k QUESTION 2 Evaluate the integral. ??¹ [(27t² - 4)i + (20t/(t²+1))j - (t/?(t²+1))k] dt 13i + 10 ln 2j + (1 + ?2)k 13i + 10 ln 2j + (1 - ?2)k 5i + 10 ln 2j + (1 - ?2)k 13i + 10 ln 2j + ((1 - ?2)/2)k
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For QUESTION 1, we need to evaluate the integral: ∫[V}-(z- dt (6t)(1 + 8i - 90j) dot (2 + 8i + 90j + t(4i + 90j)) First, we need to simplify the dot product: (6t)(1 + 8i - 90j) dot (2 + 8i + 90j + t(4i + 90j)) = (6t)(2) + (6t)(8i) + (6t)(90j) + (6t^2)(4i) + Show more…
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