Consider the function f(x) = 1 – x2. (a) Estimate the area of the region under the curve between x = 0 and x = 1 using four approximating rectangles and left endpoints. Draw the region and the approximating rectangles. Is your estimate an overestimate or underestimate? (b) Now find the exact area of the region by using the definition of the definite integral. Here are some helpful formulas from class. п(n + 1) n п(п + 1)(2n + 1) Σ с — пс. 2 i=1 i=1 i=1 (c) Check your answer for part (b) by using the "short cut" to finding the definite integral (the Fundamental Theorem of Calculus 2).

Q: Estimate the area under the graph of f(x) = 16 - r² over the interval [- 4, 1] using ten…

A:

Q: What does the integral represent in relation to the curve of a function? And what is the difference…

A:

Q: f(x) = 3/x on the intend 0<x<4

A:

Q: The Area between k*x3 and k*sin (x) is 2. What is the value of k?

A:

Q: Use the Midpoint Rule with n = 4 to approximate the value of the definite integral. Use a graphing…

A: fx=secx,  0, 1 Now, ∆x=b-an=1-04=14 Now the subintervals are 0, 14,  14, 12,  12, 34  &amp;  34, 1.…

Q: What is the area under the curve for f(x) = 3x2 +5 between x=1 and x=10?

A:

Q: se left and right endpoints and the given number of rectangles to find two approximations of the…

A: Given,         g(x)=3x2+3, 1, 3, 8 rectangles

Q: dh = For instructor's notes only. Do not write in the box below.

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.