MATH 1131Q Lecture 8: Newton's Law of Cooling and Continously Compounding Interest

8. For each of the following iterated integrals, do the following: Sketch the region of integration. Where applicable, give a geometric interpretation of the iterated integral. Evaluate each double integral. Change the order of integration where nec- essary. (a) 104 fets dydr (b)//쁩udy dr (c)//gudy @i jsdady (h)? fsinrardy (i).t{r)lydydz 0 ev 1 2 dzd @j feë´ drdy((o) 2 4x c s(y ) dydr (p)//VI阿drdy a) J sin(3戸) dydx (r) fsin(H) dzdy (s)// dady (t) 9 3 sin (㎡) drdy (u) 4 2ye'dydr (v)//e-va dydz 0 y/2 1 Vy vz 0 z ivITpdrdy@i 2向dady (y)..-75dy dr (w) (1 3)

R duire, si possible, les expressions suivantes: A = -g2 - (-9g2) B = T w times 3 C = 8 p times (-5) D = 8c - (-c) E = % times (-y) F = -4 times (-2y) G = 2 w2 - 10 w2 H = - m - 9m I = h - 3h R duire, si possible, les expressions suivantes: A = 9t times 7 B = 2 k2 - 10 k2 C = -8k times (-7 k) D = -10 u times 9 E = 10 c2 - 10 c2 F = -5y - 2y G = 10 times (-8t) H = m2 times 2 I = 6u2 times 5 = 302. R duire, si possible, les expressions suivantes: A = -10 q - 6q B = -q2 times 5 C = -g -(-3g) D = 4 k2 times 7 E = 7 t-(-6) F = 5f times (-8f) G = -8q2 times 3 H = 2 times 6v2 I = -2d times 4

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