Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. 10. f(x) = 32 - 2x: [0,8] Set up the integral (or integrals) needed to compute this area. Use the smallest possible number of integrals. Select the correct choice below and fill in the answer boxes to complete your choice. O A. dx В. 8 dx dx + С. 8 dx dx + For the interval [0,8], the area between the x-axis and f(x) is (Type an integer or a simplified fraction.)

Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [-2, 1] by…

A: Given:   fx=9-x2 over the interval -2, 1. A graph is given with three rectangles in it. To find: We…

Q: Find the area between the functions f(x)=x+2 and g(x) x from x=-1 to x 2. You must use the…

A:

Q: 1 he graph of y = and the x-axis to the right of x = 3. (If not posi (4x – 3)3/2

A:

Q: Find and evaluate exactly an integral expression that represents the area between y = f(x) and the…

A:

Q: Find the area under the given curve over the indicated interval. y = 2x; [2, 6] The area under the…

A:

Q: Set up but do not evaluate an integral that would be used to find the area enclosed by the curves…

A: Consider two continuous functions f(x) and g(x) in an interval a,b such that f(x)≥g(x) in a,b. Then…

Q: 1 2. Find the area enclosed by y = √x + 6 and y=x+2. Hint: Find the intersection of each function…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.