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Evaluate the indefinite integral as a strength series.(int frac an^-1xxdx)(f(x)=C+sum_n=0^inftyleft( dots ight))What is the radius the convergence R?
a) write the sigma notation formula because that the ideal Riemann sum (displaystyleR_n) of the role (displaystylefleft(x ight)=4-x^2) ~ above the expression (displaystyleleft<0, 2 ight>) using n subintervals of same length, and also calculate the definite integral (displaystyleint_0^2fleft(x ight)left.dx ight.) as the border of (displaystyleR_n) in ~ (displaystylen ightarrowinfty).(Reminder: (displaystylesum_k=1^nk=nfracn+12, sum_k=1^nk^2=nleft(n+1 ight)frac2n+16))b) usage the an essential Theorem of Calculus to calculation the derivative that (displaystyleFleft(x ight)=int_e^-x^xlnleft(t^2+1 ight)left.dt ight.)
Evaluate the unknown integral together an infinite series. (displaystyleintfraccosx-1xleft.dx ight.)
Evaluate the indefinite integral together a strength series. What is the radius the convergence?(displaystyleintfract1-t^8left.dt ight.)
Use the Table the Integrals to advice the integral. (Use C because that the consistent of integration.)(displaystyleint37e^74xarctanleft(e^37x ight)left.dx ight.)Inverse Trigonometric forms (92): (displaystyleintu an^-1u du=fracu^2+12 an^-1u-fracu2+C)
Use the Table the Integrals to evaluate the integral. (Use C because that the constant of integration.)(int37e^74xarctan(e^37x)dx)Inverse Trigonometric develops (92): (int u an^-1u du=fracu^2+12 an^-1u-fracu2+C)
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