To find the area that is shaded red, you find the area of the rectangle and subtract it by the area of the triangle.
Area of a rectangle:
A = l × w [ l = 11 in ; w = 6in ] Plug these numbers into the equation
A = 11 · 6
A = 66 in²
Area of a triangle:
[ b = 4 in ; h = 6 in ] Plug these #s into the equation
A = 12 in²
Area of rectangle - Area of triangle = Area of the shaded region
66 in² - 12 in ² = 54 in²
Your answer is B
The graph of is a horizontal line. So the area under
on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.
The graph of is the upper half of a circle with radius
. It's symmetric about
, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is
.
Then use the fact that the definite integral is distributive over sums, meaning