Solution11.pdf - HOMEWORK XI Calculus I Solution 1. Express...

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HOMEWORK XICalculus ISolution1. Express the limit as a definite integral on the interval [2,6]:limn+nXi=1cosx*ix*iΔxiSolution:R62cosxxdx2. Use the Midpoint Rule withn= 5 to estimate the integralR20xx+1dx. Roundthe answer to four decimal places.
3. Evaluate the integrals:(i).R3-2(x2-3)dx(iii).R1
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HOMEWORK XICalculus ISolutionZ1-1ex+1dx=Z1-1exe dx=eZ1-1exdx=e ex|1-1=e(e-1e)=e2-1(iv).R3π20|sinx|dxSolution:Z3π20|sinx|dx=Zπ20|sinx|dx+Z3π2π|sinx|dx=Zπ0sinx dx+Z3π2π-sinx dx=-cosx|π0+ cosx|3π2π= 2 + 1= 34. Find the general indefinite integralRsin 2xsinxdx
5. The velocity of a moving particle isv(t) =t2-2t-8.2
HOMEWORK XI
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