Math1011_Week14

Math1011_Week14 - Math1011 Section 5.4 11/22/2010 Evaluate...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Math1011 Section 5.4 11/22/2010 Evaluate the following definite integrals using an antiderivative. 2 0 (3 2) + x dx 1 2 (3 2) x + 2 2 /4 1c o s cos 0 x x π +
Background image of page 1

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

View Full DocumentRight Arrow Icon
Math1011 Section 5.4 1 Evaluate the integrals 2 0 (3 2) + xd x 2 22 2 2 0 (2) (0) 32 ( 2 ) ( 0 ) 6 4 x + ⎡⎤ +− + = + = ⎣⎦ 1 0 1 2 (3 2) + x [] 2 1 2 2 (1 ) (2 ) 35 2 ( 1 ) 3 2 ( 2 ) 2 6 4 −− + = = 2 2 2 /4 1c o s cos 0 x x dx π + ] 2 cos 1 cos cos 0 2 0 0 44 4 4 sec 1 tan ( t a n )( t a n 00 ) ( 1 )1 xx dx ππ + + + + = +−+ = + Evaluation Theorem If ƒ is continuous on the interval [a, b], then () b a f xd x Fb Fa =− where F is any antiderivative of ƒ, that is F’=ƒ. (Doc #1011w.54.01)
Background image of page 2
Math1011 Section 5.4 2 Find the derivative of the functions 5 () c o s = x gx td t 43 c o s = x e t t d t 2 3 22 1 =+ x s gs e x d x 2 1 3 c o s = g xt t d t
Background image of page 3

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

View Full DocumentRight Arrow Icon
Math1011 Section 5.4 2 Find the derivative of the functions 5 () c o s = x gx t d t (by Fundamental Theorem of Calculus) cosx ] 5 5 Let us show this cos sin sin sin5 0 x d dx tdt t xx = 43 c o s = x e t t d t (by Fundamental Theorem of Calculus) '( ) cos = g x 2 3 22 1 =+ x s gs e x d x (by Fundamental Theorem of Calculus plus chain rule) 2 3 2( ) 2 2 2 2 4 2 4 1 ( ) 1 ( ) 1 2 2 1 =− + +⋅ +⋅ =− + s x ss d dx e x d x e s s e s s s e s 2 s 2 1 3 c o s = g xt t d t 2 1 3 Careful, cos is a definite integral, which evalutes to a number The derivative of a number is zero '( ) 0 tt = (Doc #1011w.54.02)
Background image of page 4
Math1011 Section 5.5 3 Evaluate the indefinite integral 4 sin cos d θ θθ 2 (ln ) x dx
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/06/2010 for the course MATH 1110 taught by Professor Martin,c. during the Fall '06 term at Cornell.

Page1 / 16

Math1011_Week14 - Math1011 Section 5.4 11/22/2010 Evaluate...

This preview shows document pages 1 - 6. Sign up to view the full document.

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