Math 173 04,

the course of Dr. Mihailovs

Midterm 3

November 20, 1998

  1. Find $ \int_0^3(2x+1) \; dx$ .

  2. Find the derivative of the Fresnel function $ C(x)=\int_0^x\cos \frac{\pi t^2}{2} \; dt$ .

  3. Find the area under the graph of $ y=\cos x$ from 0 to $ \pi/2$ .

  4. Find $ \int_{-2\pi}^{2\pi}\sin (x^7+2x) \; dx$ .

  5. Find $ \int \sqrt[3]{3x+2} \; dx$ .

  6. Find $ \int \frac{(x-1)\; dx}{\cos^2 (x^2-2x+3)}$ .

  7. Find the area of the region bounded by the curves $ y=12-x^2$, $ y=2x^2$.

  8. Find the volume of the solid obtained by rotating the region under the graph of $ y=1/x$ from 1 to 10 about the $ x$-axis.

  9. Find the average value of the function $ f(x)=3\sqrt{x}+1/(2\sqrt{x})$ over the interval $ [1,4]$ .

Copyright © 1998 Aleksandrs Mihailovs