Let Ω denote the area under the curve f(x) = 4/(x^2 + 1)^3 from x = 0 to x = 1.

Q: Q1) Estimate the area under the graph of f(x) = x² + 1 from x=1 to x=3 using four approximating…

A:

Q: Estimate the area under the graph of f(x)=x^2+2x from x=3 to x=11 using 44 approximating rectangles…

A: We have to estimate the area under the graph of f(x)= x2+2x from x=3 to x=11 using 44 approximating…

Q: Approximate the area between f (x) = x² + 6x + 5 and the x -axis on the interval [0, 2] using 4…

A:

Q: y = vx from x = 0 to x = 4 and the x axis %3D

A: Given curves are  y=√x  x=0 to x=4 and the x- axis   We have to find the bounded region area .

Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

A:

Q: Find the area under the graph of y = (x + 1)^-2for x ≥ 0.

A:

Q: c) Sa* sin*x dx

A: To evaluate : The integral  ∫π43π4 sin4 x dx .

Q: Find the area between f(x) = x and g(x) = (x-2)2 %3D

A: The given two curves are fx=x  and  gx=x-22. Evaluate the intersection points of the two curves as…

Q: Find the area under the graph of f(x) = x² + 10 between x = 0 and x = Area = 6.

A: Givenf(x) = x² + 10x = 0 & x = 6

Q: find area, y=2x , y=3-x2  (0,1)

A: Area is a 2-dimensional quantity which is the measure of amount of space covered by any shape in a…

Q: Estimate the area under the curve given by the function f(x)= ^3√x on the interval [1, 8] using 6…

A: The solution are next step

Q: Find the the Yegion bounded by area y= tanx 4

A: integration gives the area of any function y .

Q: - Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12…

A: Here h = b-an = 12-04 = 3

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.