Question

Consider the following.

The x y-coordinate plane is given. A horizontal line, a curve, and a shaded region are graphed.

• The horizontal line labeled f(x) = 25 crosses the y-axisat y = 25.
• The curve g(x) = x² enters the window in the second quadrant, goes down and right becoming less steep, changes direction at the origin, goes up and right becoming more steep, passes through (5, 25) crossing the horizontal line, and exits the window in the first quadrant.
• The area below the horizontal line and above the curve in the first quadrant is shaded.

(a) Form the integral that represents the area of the shaded region.

0

  

  

  

dx
(b) Find the area of the region. (Give an exact answer. Do not round.)

Answer 1

30 125/15,25) y=25 gex)=x2 (as shaded region is the required asea bounded by the chronizontal line & the curse in the first quadrant. A = SS dydse S S dyde tot -20-K 10 -5 t + 10 15 20 25 s 15 25 0 22 +5225-32)dhe = [254 - 2375 = (125 - 15 - oto 195 (1-1) = 125 x 7 = 250 units (6) Area of the total region bounded by horizontal line yans & curve gex)=x2 is just the double of the shaded region being symmebic about 2-0 Hence, total area of the region is 2x area of shated region 2x 250 500 3 - 166.6667