I have been doing this question and I am lost as there is still something else that need to do to get the final answer,can you help me. **Evaluate the Integral**Given the integral:\[\int \frac{dt}{t^2 + t - 30}\]**Answer:**[Provide space here for students to enter their response] **Question 8: Evaluate**\[\int \frac{dt}{t^2 + t - 30}\]Rewrite the integrand:\[\frac{1}{t^2 + t - 30}\]Factor the quadratic expression:\[t^2 + t - 30 = (t + 6)(t - 5)\]Set up partial fractions:\[\frac{1}{(t-5)(t+6)} = \frac{A}{t-5} + \frac{B}{t+6}\]Multiply through by the least common denominator (LCD):\[A(t+6) + B(t-5) = 1\]Substitute convenient values for \(t\):For \(t = 5\):\[A(5+6) = 1 \Rightarrow 11A = 1 \Rightarrow A = \frac{1}{11}\]For \(t = -6\):\[B(-6-5) = 1 \Rightarrow -11B = 1 \Rightarrow B = -\frac{1}{11}\]Substitute back into the integral:\[\int \frac{1}{11(t-5)} dt - \int \frac{1}{11(t+6)} dt\]Integrate each term:\[\frac{1}{11} \ln |t-5| - \frac{1}{11} \ln |t+6| + C\]Use the properties of logarithms to combine:\[\frac{1}{11} \left( \ln |t-5| - \ln |t+6| \right) + C = \frac{1}{11} \ln \left| \frac{t-5}{t+6} \right| + C\]

Answered: Evaluate Answer: dt t² + t-30 S₁

Evaluate Answer: dt t² + t-30 S₁

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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