# 6.4_MAT_266_ONLINE_B_Spring_2020.Section_6.4.pdf - Larena...

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Larena Whitney-krugBoernerMAT266ONLINEBSpring2020Assignment Section6.4 due 03/26/2020 at 11:59pm MST1.(1 point) Use the Table of Integrals in the back of yourtextbook to evaluate the integral:Zsec3(5x)dx+CSolution:SOLUTIONFrom a table of integrals, we haveZsec3(u)du=12sec(u)tan(u)+12ln sec(u)+tan(u) +CForZsec3(5x)dx, we letu=5x,du=5dx=15du=dx, andour integral can be written asZsec3(5x)dx=15Zsec3(u)du=15h12sec(u)tan(u)+12ln sec(u)+tan(u)i+C=110sec(5x)tan(5x)+110ln sec(5x)+tan(5x) +CCorrect Answers:(1/(2*5))*(sec(5*x)*tan(5*x)+ln(abs(sec(5*x)+tan(5*x))))2.(1 point) Use the table of in Integrals in the back of yourtextbook to evaluate the integral:Zp6-4x-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 evaluateR6-4x-4x2dxwe need to complete the squareinside the radical to use the above formula.