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Calculus Solutions 12

# Calculus Solutions 12 - Answers to Odd-Numbered Problems...

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A-11 Answers to Odd-Numbered Problems 33 Jydz=Jsinh t(sinh tdt);A= isinh tcosht-Jydx;~l= ~;A=o at t=~so A= it. 41 eY = x + dm, y = In[x + d-] 47 4 ln 1% 1 49 sinh-' x (see 41) 51 -sech-'z 53\$1n3;oo 55y(x)=~coshcx;\$coshc~-\$ 57 5/' = y - 33. L( Y = 1 - y3 is satisfied by y = isech2: 92 2Y CHAPTER 7 TECHNIQUES OF INTEGRATION Section 7.1 Integration by Parts (page 287) \$(x2+1)tan-'x-%+C 21x3sinx+3x2cosx-6xsinx-6cosx+C ex(x3 - 3x2 + 6x - 6) + C 25 x tan x + ln(cos x) + C 27 -1 29 -:e-2 + 31 -2 3ln10-6+2tanV'3 35 u= xn,v=ex 37 u= xn,v=sinx 39 u= (lnx)",v=x u= xsinx,v = ex +/exsinxdx in 9 and -\$xcosxexdx. Then u= -xcosx,v = ex + ~excosxdx in 10 and - J x sin x exdx (move to left side): (x sin x - xcos x + cos x). Also try u = xex, v = - cos x. \$\$usinudu= \$(sinu-ucosu) = \$(sinx2-x2cosx2); odd 3. step function; 3ex. step function 49 0; x6(x)] - \$6(x)dx = - 1; v(x)d(z)] - I v(x)6(x)dx ~(4 = Jxl f (+x u(x) = 51," v(x)dx; +(: - \$); f for x 5 i, ~(ZX - x2 - 4) for x 2 i;: for XI i,& for x> i. u=x2,v=-cosx+-x2co~x+(2x)sinx-J2sinxdx
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