finalreviewanswers11

finalreviewanswers11 - MAC 2311, Spring 2011: Final Review...

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

View Full Document Right Arrow Icon
MAC 2311, Spring 2011: Final Review Problems and Answers Final covers lectures 1 - 35 1. Evaluate each integral: a) Z ( p x + 1) 2 p x dx b) Z cos x + sec x cot x dx c) Z csc ± csc ± ¡ sin ± (Hint: multiply each term in the fraction by sin ± .) d) Z 0 ¡ 1 = 2 3 ¡ 4 p 1 ¡ x 2 dx e) Z 1 = p 3 0 x 2 ¡ 1 x 4 ¡ 1 dx (Hint: simplify the integrand.) 2. True or false: a) If f ( x ) = e x= 8 , then Z f ( x ) dx = 8 f ( x ) + C . b) Z x 1 g 0 ( t ) dt = d dx Z x 1 g ( t ) dt c) Z f ( x ) g ( x ) dx = •Z f ( x ) dx ‚•Z g ( x ) dx 3. Evaluate each integral: a) Z ( p x + 1) 2 x dx b) Z 3 x + 3 p x 2 + 2 x + 5 dx c) Z e 4 1 ln( x 2 ) x dx d) Z e 4 1 (ln x ) 2 x dx e) Z sin(2 x ) 1 + sin 2 x dx f) Challenge! Z cos x 1 + sin 2 x dx g) Z 3csc(2 x )cot(2 x ) dx h) Z cot xdx i) Z e 1 2 x ¡ 1 (2 x ¡ 1) 2 dx j) Z 0 ¡ 4 x p x + 4 dx k) Z e 2 x e x ¡ 1 dx 4. Find the maximum and minimum values of f ( x ) = xe ¡ x on [0 ; 3] and use them to flnd upper and lower bounds for the deflnite integral Z 3 0 xe ¡ x dx . 5. Evaluate: a) d dx Z x 1 ( t ln t ) dt b) d dx Z e x 0 ( t ln t ) dt c) Z e 1 d dx ( x ln x ) dx 6. Evaluate: d dx Z 1 p x t 2 sin t 2 dt 7. If g ( x ) = Z x 1 [(ln t ) 2 + 2 t ] dt , flnd g 0 ( e ). On what intervals is
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

Page1 / 4

finalreviewanswers11 - MAC 2311, Spring 2011: Final Review...

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