Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval. x +x+2 x<1 f(x) = on [-1,3] 2x + 2 x21 The area is square units. (Simplify your answer.)

Q: Find the absolute maximum and minimum, if either exists, for the function below on the given…

A:

Q: 1. Find the local extrema of f(x) = x* – 2r2 +1, and state the intervals on which this function is…

A:

Q: Find the absolute extrema of the function on the closed interval.

A: Differentiate the function h(t)=tt+3 by using the property…

Q: What is the value of k so that the function f(x) is continuous at x=2 O-3 O - 3/2 1/2 0 1 T-2k f(x)…

A:

Q: Let f(x) = 5 + 2x2 (a) Estimate the area under the graph of f, the x-axis, and the lines x=−1 and…

A:

Q: 3x What is f'(x) given the integral function f(x) = (4u – 2) du? O f'(x) = 4x-2 %3D O f'(x) = 12x -2…

A:

Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

A:

Q: B-Test and proof the function So (x In x)² dx

A: ∫01(x logx)2dx=∫01x2 (log x)2dx use integral by parts, ∫udv=uv-∫vdu u=(logx)2…

Q: 1. The area between the graphs of f(r) = x² + x + 5 and g(1) = -r² – 21 + 14.

A:

Q: a. Find the value of (k) that make fhe fimction contimuous at x = 0 3k -3 =0

A:

Q: The shaded region shown below is bounded by the functions f (x) = - 2x2 + 2x + 10 and g(x) = 1.25x +…

A:

Q: For f(x)=3x2 +4x+5on the interval [-1, 1] estimate the area using 4 rectangles.  Do this with height…

A: The area of the function fx on the interval a,b using midpoints of the n rectangles is given by the…

Q: Use the table below to find h'(-1) for h (x) = f (g (x)). I()9() lO() 1/2 0. -2 -3 1. -1 -1 -2 -2 -2…

A: Given that hx =fgxTo find : h'-1Solution hx =fgxh'x =f'gx×g'xx=-1h'-1 =f'g-1×g'-1h'-1 =f'-2×2h'-1…

Q: Find the absolute extrema of the function on the closed interval.                   h(x) = x − 3√x,…

A: The given function on the closed interval [0,9] is

Q: Ql.a- for what value of (k) is the function y= f(x) continuous at x=2 V7x + 2- V6x +4 -2 sx and x #…

A:

Q: Find the absolute extrema of the function on the closed interval.

A: Given: fx=x2+5x,  -4,0   To Find: The absolute extrema of the function on the closed interval.

Q: 3. Let f(x) = 1.2* and g(x) = 0.92*. Identify the region for which f (x) > g(x)

A:

Q: Suppose f is a continuous positive decreasing function for x ≥ 1 and an = f(n). By drawing a…

A: To determine  Remainder Estimate for the Integral Test

Q: Find (a) the intervals of increase or decrease, (b) theintervals of concavity, and (c) the points of…

A: fx=1-xe-x Differentiating with respect to x, we get…

Q: The function fis increasing on the interval (s) (A) 0 1 © x>2 D x 2

A:

Q: Q: If f (x) is a polynomial function of the nth degree prove that fe'f(x) dx =e* {f(x)-f (x)+ f…

A:

Q: Find the local extrema of the function f(x)=xlnx.

A:

Q: The shaded region shown below is bounded by the functions f(x) = -x² + 10 and g(x) = –-1.5x + 9 and…

A: Solution:Given   f(x)=-x2+10     and      g(x)=-1.5x+9To find the area of shaded regionFormula:Area…

Q: The function f(x) = x2 – 8x + 12 is positive on (0, 2) and (6, 10) and negative on (2, 6). Find the…

A:

Q: 2) Consider the function g(x) = x³ + 3x? – 9x + 2 on the interval [-4, 2]. Find all local extrema,…

A:

Q: Find the location of the maximum absolute extremum for O A. x= 3 the function. В. X%3D0 Af(x) 6- О…

A:

Q: 64. If f(r, 0) is a constant function and the area of the region S is twice that of the region R,…

A:

Q: 2. Given the graph of the function f(x) below, use a midpoint approximation with 4 rectangles to…

A:

Q: Consider the following algebraic functions. f(x) = Vx +2 g(x) = =x + 2 Sketch the region hounded by…

A:

Q: Find the x-value corresponding to the absolute minimum value of f on the given interval. (If an…

A:

Q: The shaded region shown below is bounded by the functions f (x) = -3x2 +8 and g(x) = calculator,…

A:

Q: Find the absolute extrema of the function on the closed interval. 3 f(x) = x³ – , [-1,2]

A:

Q: Find the area of the region enclosed between f(x) = x² + 5x + 18 and g(x) = 2x2 + 2x. Area = (Note:…

A: Explanation of the answer is as follows

Q: Find f'( – 2) for f(x) = ln( (x* + 3)´) as an exact fraction or rounded to at least 2 decimal…

A:

Q: | the area of the region enclosed between f(x) x² + 3x + 20 and g(x) = 2x² + 2x. te: The graph above…

A: Please refer to the image below

Q: Find the absolute maxima and minima of the function on the given domain. f(x_ v) = 2x + 5y on the…

A: Given function f(x,y)=2x+5ywe need to find criical pointconsider f'(x)=0                     and…

Q: Find the area of the region enclosed between f(x) = x² + 10 and g(x) = 2x2 + 2x + 2. Area = (Note:…

A:

Q: Sketch the graphs of the functions. (x) = Vx and g(x) - x² 10 10 -10 5. 10 -10 10 10 -1아 y 10 -10 10…

A: To find the area enclosed by the graphs fx=xgx=x2

Q: The shaded region shown below is bounded by the functions f(x)=−x2+10f(x)=−x2+10 and…

A:

Q: 1) Find the absolute extremum values of f(x) = x2 – 2x + 9 over the interval [1, 2).

A:

Q: Find the largest interval on which the given function is increasing. a. ƒ(x) = 0 x - 2 0 + 1 b. ƒ(x)…

A:

Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 – 3x on…

A:

Q: Find the extrema of the following functions on the given interval, if there are any, and determine…

A:

Q: The shaded region shown below is bounded by the functions f (x) = -x2 + 0.5x + 10 and g(x) = -1.5x +…

A:

Q: Find an antiderivative F(x) of the function f(x) = 7x2 – 5x – 1 such that F(0) = – 4. F(x) = Preview…

A:

Q: Find the extrema of the following functions on the given interval, if there are any, and determine…

A:

Q: 9) Given the function f(x)=-3x+2 , find the net signed x-axis over the interval [-5,3]. area between…

A: Given function is  f(x)=-3x+2 We have to find the area of the region bounded by the given function…

Q: Consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2 −9x−18. Find the area, in…

A: Calculation:The given curves are f(x) = – 9 x – 9 and g(x) = x2 – 9x – 18.The area enclosed by two…

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8

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.