Date modified: Mon 2023-07-03 . 09:46 PM
Date created: Sat 2023-10-07 . 09:02 PM
# Week 3 Monday Problems Reading: 7.3. And finish reading up to 7.5. Make a cheat sheet on one normal US letter page (8.5 x 11). You may use both sides. # Problems. 1. Evaluate the following. 1. $\displaystyle \int \frac{\sqrt{4x^{2}-25}}{x}dx$ 2. $\displaystyle\int \frac{x^{3}}{\sqrt{x^{2}+9}}dx$ 3. $\displaystyle\int \frac{\sqrt{2-x^{2}}}{x^{2}}dx$ 4. $\displaystyle\int \frac{dx}{(x^{2}+9)^{3/2}}$ 5. $\displaystyle\int \frac{dx}{\sqrt{x^{2}+2x+5}}$ (Hint: Complete the square) 6. $\displaystyle\int x^{2}\sqrt{3+2x-x^{2}}dx$ 7. $\displaystyle\int \frac{x}{\sqrt{x^{2}-7}}dx$ 8. $\displaystyle\int \sqrt{x^{2}+2x}dx$ 9. $\displaystyle\int \frac{\cos(x)dx}{\sqrt{1+\sin^{2}x}}dx$. (Hint: First a $u$-substitution...then.....and then....) 10. $\displaystyle\int\sqrt{x-x^{2}}dx$ For more practice, see the section 7.3 and 7.5 in text. Also don't forget to review old material!