{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# exam1 - R(b Find the number b such that the line y = b...

This preview shows pages 1–5. Sign up to view the full content.

Name: Section Number: TA Name: Section Time: Math 20B. Midterm Exam 1 February 1, 2006 Turn off and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page of notes, but no books or other assistance on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. 1. (6 points) Evaluate the following integrals. (a) Z 3 x sin( x 2 ) dx (b) Z 3 2 x 2 x - 2 dx # Score 1 2 3 4 5 Σ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. (8 points) Let R be the region enclosed by the curves y = x 2 and y = 4. (a) Find the area of the region

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R . (b) Find the number b such that the line y = b divides the region R in part (a) into two regions with equal area. [Hint: Try integrating with respect to y rather than x .] 4 2 2-2 3. (6 points) Find the area enclosed by one loop of the polar curve r = 4 sin(2 θ ). 3 1 2 3 1 2 r = 4 sin(2t) 4. (6 points) Find the volume of a tetrahedron with height h and with a right triangular base with side lengths a and b . [Note: A tetrahedron is a pyramid with a triangular base.] h a b 5. (8 points) Let z = 1 + √ 3 i . (a) Write z in polar form. (b) Find z 10 and write it in standard ( a + bi ) form....
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

exam1 - R(b Find the number b such that the line y = b...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online