-x if x < 0 Let f (x) = x2 if x z 0

Q: Find the area of the region under the graph of the function fon the interval given. Make sure to…

A: The objective is to find the area of the region under the given graph

Q: Let a > 0 and let R be the region under the graph of f(x) =  √(9 - ax) and in the first quadrant.…

A: Points of intersection:y=x =9-axx=9-axx+ax =9x=91+aPoint (91+a, 31+a)

Q: Refer to the graph of f(x) on the interval [-2, 4] shown below. Which of the following would give…

A:

Q: (d) Prore that the function f(x) =X is Continous but not unifomly Continous on the intenal

A: Use the  absolun delta definition for uniformly continuous

Q: Suppose that f is a negative function with antiderivative F such that F(1) = 7 and F(3) = 4. What is…

A:

Q: Graph the following equation.explicitly state the equation of the asympttote, the x intercept, the y…

A: Given equations: y=-313-x+6 y=-12log2x+4-2

Q: 3. Consider the function for x +0 f(x) %3D for r = 0. (b) Divide the interval [-1, 1] into 2n parts.…

A: using trapezoidal rule

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.