Question do both Recall the definition of a definite integral: n [' rods = ΣΔΕ f(x)dx = lim f(x;)Ax n-00 i=1 where x; are right endpoints. (a) Determine Ar and x; in the definition for La (1 + 3x) dx. Ax = (b) Using the definition, evaluate the integral. L'at (1 + 3x) dx = (1 point) Suppose that the integral I endpoints and n subintervals: = 6* = f(x) dx can be represented by the following Riemann sum using right 36 1-: V30- 13 +(99* +736-(?). +...+ 7/36-(9). *: 6 6 - + n 2 on + n 11 71 (a) Determine b. b= (b) Determine f(x). f(x) = (c) Evaluate the integral by interpreting it in terms of areas. IE
VS3MI7 The Asker · Calculus
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Transcribed Image Text: Recall the definition of a definite integral: n [' rods = ΣΔΕ f(x)dx = lim f(x;)Ax n-00 i=1 where x; are right endpoints. (a) Determine Ar and x; in the definition for La (1 + 3x) dx. Ax = (b) Using the definition, evaluate the integral. L'at (1 + 3x) dx =
(1 point) Suppose that the integral I endpoints and n subintervals: = 6* = f(x) dx can be represented by the following Riemann sum using right 36 1-: V30- 13 +(99* +736-(?). +...+ 7/36-(9). *: 6 6 - + n 2 on + n 11 71 (a) Determine b. b= (b) Determine f(x). f(x) = (c) Evaluate the integral by interpreting it in terms of areas. IE
More Transcribed Image Text: Recall the definition of a definite integral: n [' rods = ΣΔΕ f(x)dx = lim f(x;)Ax n-00 i=1 where x; are right endpoints. (a) Determine Ar and x; in the definition for La (1 + 3x) dx. Ax = (b) Using the definition, evaluate the integral. L'at (1 + 3x) dx =
(1 point) Suppose that the integral I endpoints and n subintervals: = 6* = f(x) dx can be represented by the following Riemann sum using right 36 1-: V30- 13 +(99* +736-(?). +...+ 7/36-(9). *: 6 6 - + n 2 on + n 11 71 (a) Determine b. b= (b) Determine f(x). f(x) = (c) Evaluate the integral by interpreting it in terms of areas. IE
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(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