Find the area between y = 1.5x + 4 and y = decimal places. – 3. Round your limits of integration and answer to 2 10- The area between the curves is square units.

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: E. For the integral Ll- dy dr, do these three things, in order: y5 + 1 Graph (by hand) the region of…

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Q: (d) Find the area between the two curves 3 y = 1+r2 y = r² - 1

A: # We are entitled to solve one question at a time , please resubmit the other question if you wish…

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: Approximate the area under the curve graphed below from x = 2 to x = 7 using a Left Endpoint…

A: Let's find.

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

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Q: Find the area between the curves y = e-0.7x and y = 1.5x + 1 from x = 0 to x = 1.

A: Explanation of the answer is as follows

Q: Approximate the area under the curve graphed below from z = 1 to x = 6 using a Left Endpoint…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 18 –…

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Q: Q4: Find the area enclosed by the curves: y = x² and y = -x² + 4x.

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Q: Find the area between the curve of y = x + 2 and the x-axis on the inter 4 ਆਗੂਆਂ 2 4 -2- O O O 27 4…

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Q: Find the area between y=2x+3y=2x+3 and y=x2−1y=x2-1. Round your limits of integration and answer to…

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Q: 2) Find the area between the curve y ? = 2x – 5 and the line y = x – 4.

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Q: |Approximate the area between the curve below and the r-axis by computing Le on the interval [3,…

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Q: Q.8 Find the area of the curve bounded by the curves y = x* and y = 3x+4.

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Q: Q2. Find the area enclosed by the curve y = x³ – 3x² + 2x and the x-axis.

A: To find the area enclosed byy=x3-3x2+2x and x-axis

Q: It is possible for the area between two curves to be negative. (T/F)

A: Following are the answers:

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: find the t-value such that the area left of the t-value is 0.20 with 15 degrees of freedom.

A: Given that, α=0.20 df=15 The type of test is left tailed test

Q: Calculate the area between the two curves y = ax³ and y 1.4 and b = 2.4. Give your answer to three…

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Q: Find the area enclosed by the curve  x = t 2 − 2 t , y = t  and the y-axis. Round to four decimal…

A: To Determine: find the area enclosed by the curve x=t2-2t  ,y=t and the y-axis.Round to four decimal…

Q: Find the approximate area under the curve of f (x) =x+1 from x = 0 to x = 2, using 4 left-endpoint…

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Q: Find the area of the region that lies above the x-axis, below the curve z = t+ 7t + 9, y = e with…

A: We will use integration to solve this

Q: Find the area under the curve y = 14 – x and above the x-axis. Round your answer to three decimal…

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Q: Find the area between y = 5 and y = (x – 1) +1 with x > 0. If needed, round your limits of…

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Q: Find the area of the region bounded by the curve x³ x² + 2xy - y² = 0 and the line x = 4. (HINT:…

A: Given  x3 x2 + 2xy - y2 =0 x3 = (y - x )2 x3/2x = y      and   y = -x3/2x   AREA = ∫x1x21f(x)-g(x)dx…

Q: Find the area between y = 6 and y = (x – 1)´ – 3 with a > 0. If needed, round your limits of…

A: The region is bounded to y=6. Therefore,  when x=0: y=x-12-3=0-12-3=-2. Therefore, The required…

Q: Answer True or False. 5) | (x - 3) dx = the area between the x-axis 2 and the graph of y = x - 3,…

A: Given: ∫26x-3 dx = The area between the x - axis and the graph of y = x-3, over the interval [2, 6].…

Q: c. Set up the definite integral that gives the area of the region inside the circle but outside the…

A: c) The equation of the circle is, The equation of the loop is

Q: Find the area between the curves. 3x x=0, x=3, y=2 e, y=e + e 3x The area between the curves is…

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Q: 4. Find the area between the curves y = x2(x – 3) and y2 + 8y – 16x + 48 = 0

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Q: Find the​ t-value such that the area left of the​ t-value is 0.15 with 6 degrees of freedom.​

A: Given  Area to the left of t-value is 0.15 DF, n=6

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: Find the total area of the region between the curve and the x-axis 1 xs3 4 ОА. 3 O A. OB. В. О С. 3…

A: *to find:- total area.

Q: 8) Find the area of the region between the curve x = e- e15t Le-14t and the x-axis, 0 <ts In 9. y=.…

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Q: Approximate the area under the curve graphed below from x = 1 to x = 5 using a Left Endpoint…

A: We get 4 sub intervals each of width 1 unit

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: Set up the definite integral required to find the area of the region between the graph of y = x2 –…

A: Given query is to find set-up the definite Integral to find the area between two graphs.

Q: Find the area between y = 2x +2 and y x - 1. Round your limits of integration and answer to 2…

A: Solve for the area

Q: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

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Q: Find the area between y = 2 and y = (x − 1)² integration and answer to 2 decimal places. 10 9 8 6…

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Q: approximate the area under the t-curve ,with degrees of freedom 29, to the right of t=2.462

A: The degrees of freedom 29, and t=2.462

Q: Calculate the integral approximations T3 and Mg for dæ. Your answers must be accurate to 8 decimal…

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Q: 34. Find the area enclosed by the curve x = t2 – 2t, y = Vi and the y-axis.

A: Given

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

A: Find your answer below

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: Find the area between the curves y = e0.3se y = 1.9x + 1 from x = 0 to x and = 5. Area =

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Q: In the diagram below, the region between the graphs of y sin r and y= in the first quadrant, is…

A: We have to find the x-coordinate of the intersection point of these curves. sin-1x=πx2⇒x=sin πx2⇒x=1

Q: find the indefinity integral  x^9 dx

A:

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.