In Problems 21–26, use the description of the region R to evaluate the indicated
23.
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- 6. Find the area of the region bounded by x = y³ - 4y² + 3y and the x = y² - y. 77 (a) A square units 12 (b) A= square units 77 (c) A = 7/1 square units 6 (d) A= square units 71arrow_forward2)Let f(x) =2x-6 Let x0 be the x coordinate of x intercept of f(x) and y0 be the y coordinate of f(x) then x0= y0= The area of the region bounded by f(x),x axis over interval [0,x0] isarrow_forward11. Find the area of the region between the function (*)=x -*+2 and the x-axis on the x-interval [-1,2]. y= Vx-10 y = 0 12. Find the area between and between x =0 and x =9. 13. Find the area bounded by these two curves: Y =9-x? 2y = x² -3x +12 and 14. Find the area of the region bounded by these two curves: X = y" - 2y and *-y-4 =0arrow_forward
- 1. Find the area of the region bounded by y = -4x + 9, y = 2x² – 11x + 9, and the lines r = -2 and a = 5. y =-4x + 9 |y = 2x² – 11x + 9 x = -2 x = 5arrow_forward3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y 0. (0,4) (a) Set up a (sum of) definite integral(s) with respect to x that is equal to the area of R. (1,3) R (-2,0) (-1,0)arrow_forwardWhat is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis from x=-1 and x=2? ... ly = x² + 2 -1 2 13 (A) 3 25 В c) 6 D 9 B.arrow_forward
- 5. Evaluate the integral of 1 y¹/³ (x³ + 1) over the region which is bounded by the x axis, the line x = -y¹/3 and the line x = 3. f(x, y) =arrow_forward3. For the enclosed regions bounded by y = x³ – 6x and y = -2x in the graph, what is the integral that describes the enclosed regions? A. S, (x3- 6x) dx B. S, (x3 - 6x - 2x) dx C. L, (x3 - 6x) dx + -2x dx D. , (x3- 4x) dx + (-x3 + 4x) dx -2 В. -2 2 2 What is the area of the enclosed regions in problem number 3? A. 10 sq. units B. 12 sq. units C. 8 sq. units D. 4 sq. unitsarrow_forward1. Let y = x² + 1 and y = −2x + 1. (a) Graph the two functions together on the same plane. Find the points of intersection. (b) Find the area of the region bounded by the line z = −2 on the left, the line x = 2 on the right, and the graphs of the functions y = x² + 1 and y = −2x + 1.arrow_forward
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