CalcExercisesCh5

CalcExercisesCh5 - (Exercises for Section 5.1:...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
(Exercises for Section 5.1: Antiderivatives and Indefinite Integrals) E.5.1 CHAPTER 5: INTEGRALS SECTION 5.1: ANTIDERIVATIVES and INDEFINITE INTEGRALS 1) Evaluate the following indefinite integrals. You may use C , D , etc. as representing arbitrary constants. Assume that all integrands are defined [and continuous] “where we care.” a) 2 x 3 ± x 3 4 5 ± x 5 2 + 2 3 x ± 3 ² ³ ´ µ · dx ¸ b) yy dy ± c) 3 t 3 ± 2 t 2 + t t dt ² d) w + 3 () w + 4 dw ± e) 3 z 4 dz ± f) t 2 + 3 2 t 6 dt ± . Your final answer must not contain negative exponents. g) x 3 + 8 x + 2 dx ± h) 3sin x + 5cos x dx ± i) 4 cos 2 ± d ² j) sec t csc t cot t dt ±
Background image of page 1

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

View Full DocumentRight Arrow Icon
(Exercises for Section 5.1: Antiderivatives and Indefinite Integrals) E.5.2 k) sin r cos 2 r dr ± l) cot ± () 1 + cot 2 sin d ² m) 2 dx ² n) sin 5 dx ² o) a 10 + abt dt ± , if a and b represent real constants p) D x tan 5 x 4 ± ² ³ ´ dx µ 2) Evaluate D x x 5 + x dx ± . 3) For each part below, solve the differential equation subject to the given conditions. a) ± fx = 6 x 2 + 2 x ² 1 subject to: f ± 2 = 30 b) dy dx = 2 x subject to: y = 34 if x = 9 c) ±± = 3 x + 2 subject to: ± f 1 = 1 2 and f ± 1 = 7 d) d 2 y dx 2 = 7sin x + 2cos x subject to: both ( y = 10 and ± y = 4 ) if x = 0 4) Assuming that a particle is moving on a coordinate line with acceleration at = 2 ± 6 t and with initial conditions v 0 = ± 5 and s 0 = 4 , find the position function rule st for the particle. ( s is measured in feet, t is measured in minutes, v is measured in feet per minute, and a is measured in feet per minute per minute.)
Background image of page 2
(Exercises for Section 5.1: Antiderivatives and Indefinite Integrals) E.5.3 5) On Earth, a projectile is fired vertically upward from ground level with a velocity of 1600 feet per second. Ignore air resistance. Use ± 32 feet per second per second as the Earth’s [signed] gravitational constant of acceleration. a) Find the projectile’s height st () above ground t seconds after it is fired. (Your formula will be relevant up until the time at which the projectile hits the ground.) b) Find the projectile’s maximum height. 6) A brick is thrown directly downward from a height of 96 feet with an initial velocity of 16 feet per second. Use ± 32 feet per second per second as the Earth’s [signed] gravitational constant of acceleration.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/08/2011 for the course MATH 150 taught by Professor Bart during the Spring '06 term at Mesa CC.

Page1 / 11

CalcExercisesCh5 - (Exercises for Section 5.1:...

This preview shows document pages 1 - 4. Sign up to view the full document.

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