Calculus :

I have attached an example. Please fill out question 2

Description and Graph Limit of a (Right) Definite Integral Evaluate using the Riemann Sum Fundamental Theorem EX) Area under the 3- 1 SIN curve f (x) = 3x2 on Ax = n F(x) the interval [1,3] 1+i SIN 30 . R = 3 F(b) = F(3) = 33 = 27 f (xR ) = 3(1 +1 ( 2 ) 3x2dx 20 1 A; = 3 ( 1 + 1 ( 2 ) ) ( ) F(a) = F(1) = 13 = 1 n 10 Rn = [ 3( 1 +1 (2 ) ) " ( 2 ) 26 26 n F(b) - F(a) = lim -3 -2 -1 0 2 3 n-+00 [3 ( 1 +1 ( 2 ) ) ? ( 2 )2) Area under the curve f (x) = -x2+5 Ax = F ( x ) = _ on the interval [-1,2] R = F (b ) =_ f (xP ) =. 3 2 A; = F(a) = _ 1 - Rn = -3 -2 -1 2 3 F(b) - F(a) = _ -2Directions: Evaluate each Definite Integral. 3) Use the graph at the right to evaluate each of the following definite integrals: a) L',f(x ) dx = _ 22 19 b) S f ( x ) dx = - -1 2 cot 6 8 9 c) Sof (x ) dx = d) S f ( x )dx = h ) sif ( x )dx = _ e ) [of ( x ) dx = i) Sof(x )dx = n Szf ( x )dx = i S7f ( x ) dx = 8 ) S2 f ( x) dx = k ) S f ( x ) dx = _ 4) For the graph f shown above, let F(x) = _f (t) dt. Use the graph to evaluate the following: a) F(-4) = _ b) F (-2) = _ c) F(2) =