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Prepare for your exams
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Earn points by helping other students or get them with a premium plan
The calculus 2 midterm examination held on september 30, 2003. The exam covers various topics such as integration, substitution, and improper integrals. Students are required to answer questions related to defining functions, finding integrals, computing definite integrals, and determining the convergence of improper integrals.
Typology: Exams
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Instruction:Use the scratch paper provided if needed. Please keep your Answer the questions in the space provided. answers neat, brief, and to the point. Show all the steps inyour derivations.
Question 1Question 2 Question 3Question 4 Question 5Question 6 Total Please do not write in this box
QUESTION 1. Define: f (x) =^ ∫^0 x sin(t^2 ) dt, −√π < x < √π. Determine the interval(s) where f is decreasing.
QUESTION 3. Find the integral: ∫ (ln x)^2 dx.
QUESTION 4. Compute: (^) ∫ (^1) 0 x x^23 + 1dx.
QUESTION 6. Determine whether the following improper integral converges: ∫ 1 0
√x (^2) + 1 x dx.
