Use the Riemann Sum to find the area of the region bounded by the graph of f(x)=tan(x/6) and the x-axis between x = 0 and x = 2π. Write out the expression of the summation, but don’t evaluate it.

Q: Find the area betweeen y=x2 and y= -(x-1)2+1 on the interval [0,2]

A: Given: Equations of curves are y=x2 y= -(x-1)2+1 to find the area on the interval [0, 2] The area…

Q: Find the area enclosed by the graphs of a = f(y) = y³ - 26y + 10 and x = g(y) = 40 - 6y² - y³. (a)…

A: Given:The functions are  and To Find:(a) The intersection point(b) Functions that are to the right…

Q: Find the area bounded by the curve y = x² – 6x + 5 and the x-axis from -2 to 2 using %3D Riemann…

A: area bounded by curve using Riemann sum

Q: 16. Find (1) the net area and (ii) the area of the region above the x-axis bounded by y=121-x².…

A:

Q: What is the integral of x(x + 2) dx? A. x³/3 + x2 + C B. x³/3 + x²/2 C. (x+2)/2 D. x³/3 + x²/2 + C

A: We know, ∫xndx= x(n+1)/(n+1) , for any real number n

Q: Find the area of the region bounded by f(x) = a√bx - c the x -axis and the line x = 11 using Right…

A: Given: Here is the given data, fx=abx-c Where, x=11a=4.68b=4c=7 To find: The area of the region…

Q: Q1/ a) Sketch the graph of y = sin2x for 0 <x SI %3D b) find the total area bounded by the curve and…

A: This is a problem related to calculating area under curve of the polar equation. Based on the…

Q: Use rectangles to estimate the area under the graph of ƒ(x) = 4 − x², above the x-axis and from x =…

A:

Q: Find the area of the region between the graphs of y = 15 – x² and y = - 3x + 5 over the interval 0 <…

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Q: Let f(x) = x^2 − 2 and g(x) = x^3 − 2. a. Solve for any intersection of f and g. b. Draw the region…

A:

Q: Set up the Riemann Sum which represents the area under the curve y = x³ - 2x + 1 from x = 2 to x =…

A: The given curve is  and the interval is  .  .  .

Q: Partition [0,pi] into four equal partsand calculate the lower and upper sums for g(x)=2sinx.  What…

A: The Left Riemann Sum (also Left Endpoint Approximation) uses the left endpoints of a sub interval:

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.