8.1ByPartsSolutions

8.1ByPartsSolutions - MthSc 108-Learning Activity Solutions Section 8.1 Integration by Parts 1 log 2 x dx(Hint First use a property to rewrite the

This preview shows pages 1–3. Sign up to view the full content.

MthSc 108-Learning Activity Solutions Section 8.1: Integration by Parts 1. 2 log xdx (Hint: First use a property to rewrite the integrand.) Solution: First note that 2 ln log ln 2 x x = . Now let ln ux = . Then 1 du dx x = . Let dv dx = and then vx = . 2 22 ln 1 1 1 log ln ln ln 2 ln 2 ln 2 1l n ln ln 2 ln 2 ln 2 log log ln 2 x x dx dx xdx x x x dx x xx xx d x x C x x x C  == =   =− = + + ∫∫ 2. Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve x ye = , and the line 1 x = about the y-axis. (Hint: Use the shell method.) Solution: 1 0 2 x Vx e d x π = Now let = . Then du dx = . Let x dv e dx = and then x ve . V = 2 xe x dx 0 1 = 2 xe x 0 1 + e x dx 0 1 = 2 1 e +− e x 0 1 = 2 1 e 1 e + 1 = 2 4 e V = 2 4 e cubic units

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

View Full Document
3. Find the volume of the solid generated by revolving the region bounded by the x-axis and the curve sin yx x = , 0 x π ≤≤ , about the y-axis. (Hint: Use the shell
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/30/2011 for the course MTHSC 108 taught by Professor Any during the Spring '08 term at Clemson.

Page1 / 5

8.1ByPartsSolutions - MthSc 108-Learning Activity Solutions Section 8.1 Integration by Parts 1 log 2 x dx(Hint First use a property to rewrite the

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online