Express the limit as a definite integral. n 8 lim 2 cAxK, where P is a partition of [6,14] ||P||→0 k=1 The definite integral is

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

A: For A(1), The graph is bounded between the horizontal and vertical axis. Between t=0 to t=1, The…

Q: 2x Let f (x) = x+3 Then f is increasing over R*. False True

A: We will check for the sign of first derivative If f'(x)≥0 , then f(x) is increasing If f'(x)≤0 ,…

Q: Express the limit lim > ||P|→0k=1 c- 4ck) Axk, where P is a partition of [-6,8], as a definite…

A:

Q: Part. f. True or False: g(x) = In(x-1) is continuous for x > 1. 4 x +22

A:

Q: Write the limit as a definite integral on the given interval, where c; is any point in the ith…

A:

Q: 8 Express the limit_lim Σ (ck-4ck) Axk, where P is a partition of [ – 6,9], as a definite integral.…

A:

Q: Which of the following is the domain of f(x, y) = ln(9-x² - y²)? Ox² + y² ≤9 Ox² + y² ≥9 00< x² + y²…

A: To find the domain of the following function.

Q: III (20') Let X={1, 2, ..., 16} and define function f(x)=rx for all x € X where rx is the remainder…

A: Function f(x) = rx  where rx is the remainder when 3x is divided by 15. When x=1 We have rx the…

Q: Let A(z) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

A:

Q: Consider the area between the function f(x)=-4x and the x-axis on the interval I=[0,3) Answer…

A: Given that : The function f(x)=-4x Interval = 0,3 in closed

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.