Consider the area under the graph of f (x)=x – 3x, from x = 2 to x= 4. a. Estimate the area under the graph, on the given interval, by using 4 rectangles and left endpoints, L.

Q: ii, Find the area under the graph y=5x⁴between the limits x= 1 and x=3.

A:

Q: Given the function y z²+z+1.5, determine the area under the curve from the y-axis to the point where…

A: Given Function

Q: The following is a Competing Species model: (3 [ x′ (t) = x (³ − ¾ − ³) ly(t)= y(t)= y(5-x - y)

A: The  given system  is   Then, the above  sytem becomes : Now, the  critical  point  of the  above…

Q: Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

A: We use integration to find the area.

Q: Find the area under the graph of y = 2x² - 2x + 4 on the interval [-2,0].

A: y=2x2−2x+4 on the interval [−2,0]

Q: Approximate the area under the graph of f(x) and above the x-axis using n right rectangles. f(x) =…

A: This question is about application of reminam intergal

Q: Find the area bounded by the curve f(x) = -x² + 10 and the x-axis. Give your answer correct to two…

A:

Q: Graph the function in the given interval. Then find the total area of the region between the curve…

A:

Q: Estimate the area under the graph of f(x) = 1 + x 2 from x = −1 to x = 2 using three rectangles and…

A: To find the area under the graph of f(x)=1+x2 from x = −1 to x = 2 using three rectangles and right…

Q: Find the area bounded by the curve f(x) = -x² + 7 and the x-axis. Give your answer correct to two…

A: We have to find Area bounded by the given curve and x-axis.

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.