In a right triangle, the hypotenuse / the opposite side is:
1 answer:
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First, recall that Gaussian quadrature is based around integrating a function over the interval [-1,1], so transform the function argument accordingly to change the integral over [1,5] to an equivalent one over [-1,1].
So,
Let
. With 
, we're looking for coefficients 
and nodes 
, with 
, such that
You can either try solving for each with the help of a calculator, or look up the values of the weights and nodes (they're extensively tabulated, and I'll include a link to one such reference).
Using the quadrature, we then have
So,
Let
You can either try solving for each with the help of a calculator, or look up the values of the weights and nodes (they're extensively tabulated, and I'll include a link to one such reference).
Using the quadrature, we then have
The area of the shaded region in the given image is: 1,111.84 ft²
<h3>How to Find the Area of a Shaded Region?</h3>To find the area of the shaded region in the image given, find the areas of the unshaded region, then subtract it from the total area of the whole figure.
Area of the total figure = area of two semicircles + area of the rectangle.
Dimensions of the rectangle is given as, 18ft x 22ft.
Area of the rectangle = 18ft × 22ft = 396 ft²
The diameter of each of the semicircle = 7 + 7 + 18 = 32 ft
The radius of each of the semicircle = 1/2(32) = 16 ft
Area of the two semicircles = 2(1/2 × πr²) = 2(1/2 × 3.14 × 16²)
Area of the two semicircles = 803.84 ft²
Area of the rectangle = 32 × 22 = 704 ft²
The total area = 704 + 803.84
The total area = 1,507.84 ft²
The area of the shaded region = 1,507.84 - 396
The area of the shaded region = 1,111.84 ft²
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