MAT223H1 Lecture 15: Lecture 15.pdf

Integrate the following a. f(x)=e [2+e b, f(x)= e_ + e k. f(x)= - 2 16 3 x 4 1/2 2 3 x 1 2 X 2 cos( 7 x ) 6 sin 7 x) cos( In x) c. f(x)= [e +1] m.) f(x) 3 x d. f(x)= e sec( e ) tan( e n. f(x)= exp( 4x ) e· f(x)= 1/3 o) f(x) tan( 2x ) t exp 4x 3 ] P. f(x)= 1 / [ x ln( x ) ] 3 x -3x 2 f. f(x)=e[e + e 3 x q. f(x)= f(x) = 42 x 3 x t 1 4 3 In 2 x) 1n( e 5 r. f(x) = . h, f(x)= ( x + e) 2 i·f(x) = 5xexp( 3 x +1) s) f(x)= sec( 5x ) -4x 2 2 j, f( x)= ( e

Let T : V -* F be a linear map. Prove that if there is u 0 nullT. V = nullT" span(u). Hint: For each v V, find c F for which T(v cu) = 6.