do both

Community Answer

(a) quadint_(a)^(b)f(x)*dx=lim_(n rarr oo)sum_(i=1)^(n)f(x_(1))Delta x.{:[" Here "int_(-1)^(5)(1+3x)*dx quad=-(12 )/(n)sum_(i=1)^(n)(1)+(108)/(n^(2))sum_(i=1)^(n)(i)],[=>a=-1","b=5" and "f(x)=1+3x quad=-(12 )/(n)(n)+(108)/(n^(2))((n(n+1))/(2))],[Delta x=(b-a)/(n)=(5-(-1))/(n)quad=-12+54((n+1)/(n))],[Delta x=(6)/(n)],[=-12+54(1+(1)/(n))],[" Thus "],[x_(i)=a+i Delta x],[x_(i)=-1+i((6)/(n))],[x_(i)=-1+(6i)/(n)],[{:[int_(-1)^(5)(1+3x)dx=lim_(n rarr oo)sum_(i=1)^(n)f(x_(i) ... See the full answer