Practice Exam: Techniques of Integration

Practice Exam: Techniques of Integration
Time: 60 minutes

Problem 1 (15 points) Compute the exact value of $\displaystyle \int_0^\pi \sin^2(\theta)\,d\theta$

Problem 2 (10 points) Compute the exact value of $\displaystyle \int_1^3 \frac{\ln (2x)}{x^2}\,dx$

Problem 3 (15 points) Find $\displaystyle \int e^{-2t}\cos t\,dt$

Problem 4 (10 points) Find $\displaystyle \int \frac{3x^3-17x^2+36x-35}{x^2-4x+4}\,dx$

Problem 5 (10 points) Find $\displaystyle \int \tan^4(s)\sec^4(s)\,ds$

Problem 6 (15 points) Find $\displaystyle \int\arcsin (x-1)\,dx$

Problem 7 (10 points) Find $\displaystyle \int \sqrt{9-4x^2}\,dx$

Problem 8 (15 points) Find $\displaystyle \int\frac{2x-1}{x^2-2x+10}\,dx$

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