# 6.4 Webwork.pdf - William Forbes Assignment Section 6.4 due...

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William ForbesSharmaMAT266ONLINEASpring2018Assignment Section6.4 due 01/19/2018 at 11:59pm MST1.(1 point) Use the Table of Integrals in the back of yourtextbook to evaluate the integral:Zsec3(6x)dx+CSolution:SOLUTIONFrom a table of integrals, we haveZsec3(u)du=12sec(u)tan(u)+12ln sec(u)+tan(u) +CForZsec3(6x)dx, we letu=6x,du=6dx=16du=dx, andour integral can be written asZsec3(6x)dx=16Zsec3(u)du=16h12sec(u)tan(u)+12ln sec(u)+tan(u)i+C=112sec(6x)tan(6x)+112ln sec(6x)+tan(6x) +C2.(1 point) Use the table of in Integrals in the back of yourtextbook to evaluate the integral:Zp10-4x-4x2dxNote: Use an upper-case ”C” for the constant of integration.Solution:SOLUTIONFrom a table of integrals, we haveZpa2-u2du=12upa2-u2+12a2sin-1ua+CTo evaluateR10-4x-4x2dxwe need to complete the squareinside the radical to use the above formula.10-4x-4x2=-4(x2+x)+10=-4(x2+x+14-14)+10=-4(x2+x+14)-4(-14)+10=11-4(x+12)2=11-(2x+1)2We havea2=11=a