midterm sample

midterm sample - Math 1B Sample First Midterm π 1. (5...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 1B Sample First Midterm π 1. (5 points) Estimate the integral sin x using Simpson’s rule with n = 6. 0 2. 4 (6 points) Find 0 ∞ 3. (6 points) Find 0 4. ln x √ dx x arctan x dx (1 + x2 ) (π /2)2 − (arctan x)2 (6 points) Determine whether the series find the sum. . Be careful to explain your steps. ∞ 3n + 5n converges or diverges. If it converges, 15n n=1 5. (7 points) Find the area of the surface obtained by rotating the curve y = ex , 0 ≤ x ≤ ln 2, about the x-axis. 6. (8 points) Find 5x2 − 5x + 5 dx. x3 − 2x2 + x − 2 7. (12 points) Find two of the following six integrals: [Caution: some of these integrals are impossible! ] (a). (b). (c). • • • • dx ln x √ sin x dx 3 x2 + 1 dx (d). sin2 x dx cos4 x (e). ex ln x dx (f). x x2 + 4x + 13 dx Be sure to circle the ones you want credit for. “Divergent” is an acceptable answer, but say why it diverges. “Impossible” is not an acceptable answer. Don’t forget the formulas on page 2. Some Formulas Trigonometric Identities 1. sin2 x = 1 (1 − cos 2x) 2 2. cos2 x = 1 (1 + cos 2x) 2 3. sin A cos B = 1 sin(A − B ) + sin(A + B ) 2 4. sin A sin B = 1 cos(A − B ) − cos(A + B ) 2 5. cos A cos B = 1 cos(A − B ) + cos(A + B ) 2 Trigonometric Integrals 6. u sin u du = sin u − u cos u + C 7. u cos u du = cos u + u sin u + C 8. un sin u du = −un cos u + n 9. un cos u du = un sin u − n 11. 12. 13. 14. un−1 sin u du a2 + u2 u a2 a2 + u2 du = a2 + u2 + ln |u + a2 + u2 | + C 2 2 1 u a2 + u2 du = (a2 + u2 )3/2 + C 3 u a4 u2 a2 + u2 du = (a2 + 2u2 ) a2 + u2 − ln |u + a2 + u2 | + C 8 8 √ √ a2 + u2 a + a2 + u2 du = a2 + u2 − a ln +C u u √ √ a2 + u2 a2 + u2 du = − + ln |u + a2 + u2 | + C u2 u Integrals Involving 10. √ un−1 cos u du ...
View Full Document

This note was uploaded on 02/19/2012 for the course MATH 1 taught by Professor Wilkening during the Spring '08 term at Berkeley.

Page1 / 2

midterm sample - Math 1B Sample First Midterm π 1. (5...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online