Question

Divide given [a,b] into n equal subinterval. (a) Draw the curve and the inscribed partitions or rectangles and compute the sum of the areas (b) draw the curve and the circumscribed partitions or rectangles and compute the sum of the areas. f(x) = – x2 + 25; (0,5); n = 5

Answer 1

81 f(") - x² + 25 [0]; nos fo Soln from the given function it is clear that it is a parabolic graph. f(0) = 25 f (5) - 25+ 25 graph will be. (6,257 -ntrs

Now part (a) inscribed partition or rectangle and compute sum. $3,16) su, 9) 1 2 3 4(5,8). inscribed area = Area of (t + 2+ 3+) © 2UXI 21%] + 16X1 +381 arut21f16f5 a 70 squnea inscribed area = 70 sq unei

or (ь circumscribed partition rectangle & sum of area (6,25) , 16) er, s) (6,5) 2 5 area - sum of circumscribed q 1, 2,3, rectangular area 4 ss. - 25xit aux 1 +21 + 16 + 9 95 89 unit ed area = 95 squaith circumscrib