Consider the following. y y = f(x) (a) By reading values from the given graph of f, use five rectangles to find a lower estimate for the area under the given graph of f from x = 0 to x = 10. (Round your answer to one decimal place.)

Q: 32 y = f\x) 16 16 32 x rectangles to find estimates of each type for the area under the given graph…

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Q: Find the area between the graph of the given function and the x-axis over the given interval, if…

A: ∫x1+x22 dx Put  1+x2=t⇒0+2x=dtdx⇒2x dx=dt⇒x dx=dt2 Therefore, ∫x1+x22 dx=∫dt2t2=12∫t-2…

Q: How many individual areas in the total area bounded by the curve y=x - 3x +2x and by the x-axis from…

A: first we plot the given region then decide how many areas exist

Q: Use the graph shown below to estimate | f(x)dx. 8 4 2 2 4 6 8 This integral represents the area…

A: Let's find area from given graph.

Q: Find the area between the curves of the functions f(x) =x+1 and g(x)= x². Round to 1 decimal when…

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Q: 1 f(x) =; 1+ 7. Find the area under the curve

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Q: Approximate the area under the curve of f(x) = e? over the interval %3D [0,4] using 4 rectangles and…

A: Given that  f(x)=ex   over the interval 0,4               &    n=4 rectangles Since, we know…

Q: 3 Find the area under the curve y over the interval [0, 4]. (2x + 5)? Enter the exact answer. area =

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Q: If you want to approximate the area under a positive curve y=f(x), from x=-5 to x=6, using 7…

A: The given question can be solved as shown in step2.

Q: Do the following. (Round your answers to four decimal places.) (a) Estimate the area under the…

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Q: Find the exact area between the curve y = e* – 2 and the x-axis for 0 sxs2. |

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Q: For the area enclosed between the curves of the equation f (x) = x and g (x) = k to be 30 (ul), a…

A: here we have to find the intersection points compare both functions  so upper and lower limit…

Q: Let a denote a positive constant. If the area under the curve y = x√(2ax - x2) from x = 0 to x = a…

A: We have to find the value of a so that area under the curve y=x2ax-x2 from x=0 to a is equal to 888

Q: Find the area between the graph of y = and the x-axis for x e [0, b] where b is a (2x2 + 1)2…

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Q: Consider the function f (x) = -x² + 3x + 9. What is the overestimate of the area under the curve of…

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Q: rval [1,4] approxim

A: Here we have to find the area between g(x)=ex2 and the x-axis by finding  n = 4 using the left…

Q: Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

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Q: Find the exact area under the curve between the indicated values of x. 3 ; between x = 1 and x = 3

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Q: Find the exact area under the curve between the indicated values of x. y = -x2 + 9; between x = 0…

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Q: (a) Estimate the area under the graph of f(x) = 2 + 4x from x = -1 to x = 2 using three rectangles…

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Q: 8. Find the area under the curve y = e* and above the x-axis from x = 0 to x=1. -3x

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Q: Consider the following. y y = fix) 4 8 (a) By reading values from the given graph of f, use five…

A: Form the given information, n=5 and a=0 and b=10. Obtain the value of ∆x. ∆x=b-an=10-05=2 Divide the…

Q: For the following graph of a function, estimate the area under the curve on the interval [-4, -1]…

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Q: 10 Determine the area above f(x)=x²+2x+3 and below the line y=11.

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Q: For the following graph of a function, estimate the area under the curve in the interval [-5, 1]…

A: Given interval [ - 5 , 1 ] divide in 3 interval △x=1-(-5)3=2 -5 , -3 , -1 , 1 For midpoint…

Q: approximate the area under the graph of f(x) and above the x-axis using the following methods with n…

A: Your question has four sub parts. I have answered the first three sub parts. Please post the balance…

Q: Find the area between the curves of the following functions. First graph, then find the area. The…

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Q: approximate the area under the graph of f(x) and above the x-axis using the following methods with n…

A: (a)To approximate the area under the graph of f(x) and above the x axis, using n = 4 and left end…

Q: Approximate the area under the curve graphed below from x = approximation with 5 subdivisions. 3 to…

A: From the given graph

Q: Do the following. (Round your answers to four decimal places.) (a) Estimate the area under the…

A: Given, fx=2+2x2 from x=-1 and x=2

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

A: Width of each interval = (6-2)/4= 4/4= 1 So the partition is 2 , 3, 4, 5, 6 So the midpoints are 2.5…

Q: Find the area between the curve y = 1/x7° and the x-axis from x = 1 to co. square units

A: Given: The area between the curve y=1x76 from x=1 to ∞ To find the area of the curve. The formula…

Q: (a) Estimate the area under the graph of f(x) = 5/x from x = 0 to x = 4 using four approximating…

A: Given function is  We divide the interval [0,4] into four sub-intervals and length of each…

Q: What is the area enclosed between the graphs of x=y2 and x=-3y+4? Round to the nearest hundredth.

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Q: Find a formula for the area A(w) of the triangle bounded by the tangent line to the graph of y = ln…

A: Given  y=ln x11y=11(lnx) We need to find out the tangent line. First we find out the slope To find…

Q: 1. Find the area in the first quadrant bounded by f (x) = 4x- x and the x-axis.

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 1. ts) For the function f (x) = sin x, find the net area of the region between the curve and the x-…

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Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

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Q: Given the graph of the function f(x) below, use a midpoint approximation with 3 rectangles to…

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Q: 4. Given f(x) = e* + 2, approximate the area under the graph of f(x) and above the x-axis from x = 0…

A: Answer is mentioned below

Q: Find the exact area between the curve f (x) = x³, the x-axis, and x=0 and x=4.

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Q: For the following graph of a function, estimate the area under the curve on the interval [-6, –1]…

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Q: approximate the area under the graph of f(x) and above the x-axis using the following methods with n…

A: To calculate (a) the area under the graph of f(x) and above the x-axis by using the left endpoint…

Q: What is the area between the graphs of f (x) = 3/x+7 and g (x) = x – 2 on the interval [0, 16]?…

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Q: For the following graph of a function, estimate the area under the curve on the interval [-2, 6]…

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Q: 10. Find the area between the graph of y = and the x-axis for x E [0, b|] where b is a (2x² + 1)²…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the area of the “triangular” region in the first quadrant that is bounded above by the curve y…

A: Find the area of the “triangular” region in the first quadrant that isbounded above by the curve y =…

Q: approximate the area under the graph of f(x) and above the x-axis using the following methods with n…

A: Ypu have asked a question with four sub parts. I have answered the first three sub parts. Please…

Q: (8) Find the area under the curve f(x) = e* – 1 from X =1 to x 2 Leave the answer with e, don't use…

A: SOLUTION-

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.