\fX X The graph of f is shown in the figure. Let A(x) = I f(t) dt and F(x)= If(t) dt be two area functions for f. Evaluate the following area 8 Area=17 4 Area=7 =2 functions. a.A(-2) b.F(8) c.A@4) d.F@d) e.A@) -44 Area=10 a.A(-2)= (Simplify your answer.) Consider the function f(t) =t + 9 and real number a = - 9 (see figure). X a. Find and graph the area function A(x) = If(t) dt. b. Verify that A'(x) = f(x). : a. Find the area function. AX)= Evaluate the following integral using the Fundamental Theorem of Calculus. Explain why the result is consistent with the figure. y= x2 - 4x + 9 J (x2 - 4X +9) dx 0 X . . . (x2 -4x +9) dx = (Type an exact answer.)Evaluate the following integral using the Fundamental Theorem of Calculus. Sketch the graph of the integrand and shade the region whose net area you have found. (x2 + 3x -4) dx - 4 . . . (x2 +3x -4) dx= (Simplify your answer.) - 4Evaluate the following integral using the Fundamental Theorem of Calculus. (t_ 3. 9) dt= |:| (Type an exact answer.) Evaluate the following integral using the Fundamental Theorem of Calculus. 12 (8-x)(x- 12) dx 8 . . . 12 (8 -x)(x - 12) dx = 8 (Type an exact answer.)Use the Fundamental Theorem of Calculus to evaluate the following definite integral. V3 2 5 dx 0 V1-X . . . 1 3 N 5 dx 1/1 -x2 (Type an exact answer.)\fEvaluate the following definite integral using the Fundamental Theorem of Calculus. 216 . . . 216 yay= (Type an integer or a simplified fraction. )Evaluate the following definite integral using the fundamental theorem of calculus. 3 2 J'z +5 dz z 1 T J'22 = dz= T t . z= |:| (Type an exact answer.) T Find the net area and the area of the region bounded by y = 2 cos x and the x-axis between x= - 2 and x = . Graph the function and find the region indicated in this question. The net area is D (Simplify your answer.) Find the area of the region bounded by the graph of f and the x-axis on the given interval. f(x) =X - 20: [2,3] _ e e0 0 0 0 GO The area is D (Type an integer or a simplified fraction.) \f\f\fX Match the functions f whose graphs are given in (a)-(d) with the area functions A(x) = f(t)dt, whose graphs are given in (A)-(D). Ay O Ay + y = f(t) Ay + Ay y = f(t) y = f(t) y = f(t) O t h (a) (b) (c) (d) . . . Ay Ay Ay + y = A(t) Ay + y = A(t) t y = A(t) y = A(t) b o b h (A) (B) (C) (D) a = b = C = and d = (Type A, B, C, or D.)Consider the graph of f shown to the right. X a. Estimate the zero(s) of the area function A(x) = If(t) dt for0