## Calculus Practice Exams

Problem 1. Evaluate Answer. This is a definite integral. One way to handle it is to find an antiderivative of and then evaluate the result at 0 and .
Use integration by parts technique. Set This gives The technique of integrating rational functions gives After easy calculations, we get Now that we have the antiderivative we use it to get Problem 2. Evaluate Answer. We will use Substitution Techniques. Set We have . The new integral is The technique of integrating rational functions gives Since we have Do not forget to go back to the variable x, we have Problem 3. Evaluate Answer. Note that this integral is direct from the formula Indeed, if we let , then we have in other words, we have On the other hand, we may want to use the technique of integrating rational functions of and . Let us show the main points of this technique on this example for the sake of being somehow more complete!!!

Set . Then we have This gives Easy algebraic computations yield: Since then we have Back to the variable x, we have Using the half-angle formula for the cosine we obtain and thus finally Problem 4. Evaluate Answer. If we complete the square we get which suggests the substitution . Hence . Therefore we have Back to the variable x, we get Problem 5. Evaluate  We have and Putting the two together we get [Next Exam] [Calculus] [CyberExam] S.O.S MATH: Home Page

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