(a) Approximate integral^7 0 root 98 ? x^2 dx for n = 5 using the left, right, t
ID: 2835529 • Letter: #
Question
(a) Approximate integral^7 0 root 98 ? x^2 dx for n = 5 using the left, right, trapezoid, and midpoint rules. (Round your answer to five decimal places.) Left (5) approx Right (5) approx. Trap (5) approx. Mid (5) approx (b) Find the exact value of integral^7 0 root 98 ? x^2 dx geometrically. The graph of y = root 98 ? x^2 is the upper half of a circle of radius centered at the origin. The integral represents the area under this curve between the lines x = 0 and x = The area can be written as the sum of the areas of a half a fourth an eighth a sixteenth of a circle and an isosceles triangle a square a rectangle a trapezoid The exact area is.Explanation / Answer
(a)
LEFT(5) =7/5( f(0)+f(7/5)+f(14/5)+f(21/5)+f(28/5)) ~ 64.851448897
RIGHT(5) = 7/5 ( f(7/5)+f(14/5) + f(21/5)+f(28/5)+f(7)) ~ 60.7921559
TRAP(5) = 7/10* (f(0)+2f(7/5)+2f(14/5)+2f(21/5)+2f(28/5)+f(7)) ~ 62.8218024
MID(5) = 7/5*( f(7/10)+f(21/10)+f(35/10)+f(49/10)+f(63/10)) ~ 63.0656316
(b)
Radius is sqrt(98) = 7 * sqrt(2)
x=0 to x=7
Eight of a circle (of radius 7*sqrt(2)) and of a rectangle (of size 7*7/2)
Area is then [Pi* (49*2) / 8] + [49/2 ] = 49/4(2+Pi)
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