|-4 Find the area of the shaded region. 3. yA 4. yA x= y? – 4y x= y? - 2 y=1 (-3, 3) x=e y=-1 x= 2y – y?

Q: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11. 4. Determine the area to…

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Q: 3. Find the area of the region enclosed by the curves y = x² + 2, y = -x, x = 0, and x = 1. (a) (c)…

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Q: ニ1 近。 Question 2 D. O E OA 3. (A) 3. 3. (). 32 3. (C) 16. (B) zg (7) The area of the region enclosed…

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Q: (f) Find the area enclosed between the line y = 3x and the curve y? = 25x. Calculate the area…

A: Only one question allowed to be solved at a time . I have solved 2 and included hints for third…

Q: 3. Find the z= 4 a. area bounded by the curve ay² = z* and the line Ans. 141 a².

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Q: 1) Find the area of the shaded region: yA (1, e), y= e* y= xe** а.

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Q: The area of the region bounded by x - /9- y, the y-axis and the line x-y in the first quadrant is:…

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Q: 2. S(r2 +r + 1)e"dr 3. Find the area of the region in th

A: Given problem:- ∫ (r2+r+1)er dr

Q: Solve this attachment.

A: From the figure, the integral to obtain the area can be represented as, ∫-11y2-2-eydy

Q: Find the area between the y-axis and the graph X = Y 7 6 5 4 X 543-2/1² 1 2 3 4 5 WŃ y - 1 on the…

A: Here we have to use the concept of integration

Q: What is the area of the region bounded above by y= sin x below by y=x- T and from the left by the…

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Q: Find the area of the shaded region. (-5е — 5) 2 y 14 (1, 5e) 12 10 y = 5 e 8 6. 2 y = 5xe -1.0 -0.5…

A: The area of the given shaded region which is bounded by the curve y=5ex , y=5xex2  and x=0  is…

Q: Find the area of the region bounded by the graph of y = 4 – 2² and the r-axis. (4 - .2 b. (4 – 2²)dz…

A: The equation of the given curve is y=4-x2 We need to find the x-intercept of the curve,…

Q: Find the area of the shaded region. y x = y - 7 y = 1 x = ey -4 -8 -2 2 4 -6 y = -1 -2 -3 2.

A: We have to find the area with respect to y here. To find the area between x=e^y and x=y^2-7 we have…

Q: 1. Find the area within the curves y-25-x', 256x = 3y', and 16y 9x. A. 37.26 units B. 37.62 units C.…

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Q: o. Find the area of the region bounded by the curve y =x csc²x, the x axis 1 and the lines x = 1 =t…

A: Answer and explanation is given below

Q: 4 Evaluate [4y -7y-12 у' - у - бу 4 5 Find the area between the curve x? = 4ay, the x-axis, and the…

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Q: The area of the region bounded by y-19-x, the x-axis and the line y-x in the first quadrant is: O…

A: Given: y=9-x2 y=0 y=x Calculation: Use an online graphing calculatora and obtaine the bounded region…

Q: Qy y=x-1; y=9-x² Find the area them for メニー2 ; メ-\ between

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Q: Find the area of the shaded region. y 14 (1, 5e) 12 10 y= 5 e 8 2 y= 5 xe -1.0 -0.5 0.5 1.0 1.5 2.0

A: Given,  The graph of  y = 5ex  and  y=5xex2  Point of intersection of the graph is 1, 5e  We have to…

Q: The area bounded by the curve y = 3/T and the lines e = 5 and a = 9 above the a – axis is square…

A: First of all find all meeting points then calculate the area.

Q: 3. The area of the region under the curve y = 6z bounded by the lines z = 3 and z = 5 above the…

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Q: Find the area of the shaded region below. yA x= y² – 4y (-3, 3) x = 2y – y² X :

A: The region is bounded by the graphs x=2y-y2 and x=y2-4y

Q: Find the area of the shaded region. У 14 (1, 5e) 12 10- y = 5 e* y = 5x e х -0.5 0.5 1.0 1.5 2.0…

A: The area of the shaded region can be calculated using  integration. The following integral is set up…

Q: problem in photo attached

A: Given:

Q: 10- dA Where D is the region in the first quadrant bounded by D 2y-y2 x? = 4 – 2y. ein v

A: Using horizontal strip evaluate limit of the integral

Q: 17-Graph of the function y = x^3 What is the area of the region bounded by the lines y = 0, y =1 and…

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Q: Find the area of the shaded region. 2 x = y? - 9 fy=1 x= ey -10 -8 -6 -4 -2 2 4 y= -1

A: This question is solved by concept of double integral.

Q: Find the area of the shaded region. y 3- x= y - 8 y = 1 x= e X -6 -4 -2 4 Hy = -1 -2 -3 2. 2.

A: To find area of a shaded region we always draw a strips parallel to either x axis or y axis…

Q: 2 Find the area of the region bounded by the curve y2 =4x and the lines x = 1 and x = 4. A. 24…

A: Given y2=4x X=1 and x=4

Q: Let Rbe the region in the first quadrant under the graph of y = for 0 SaS V6. 22+2 (a) Find the area…

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Q: 4. x= y² – 4y (-3, 3) -4 Find the area of the shaded region. x= 2y – y?

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Q: Find the area of the shaded region. y 14 (1,5e) 12 1아 y-5e/ 8 4 y = 5 xe -1.0 -0.5 0.5 1.0 1.5 2.0…

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Q: 4. Find the area of the shaded regions. YA y= Vx+ 2 x= 2 x+1 (a) YA x = y² – 4y (-3, 3)* x = 2y – y²…

A: since you have posted multiple questions, so I'll solve first one for you , for rest question's…

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: Find the area of the shaded region y = 5x-x² y=x 1 (a) (4,4) YA x=y²-2 y=-11 1 (b) y=1 x=e²

A: 1aThe area is bounded by the curves y=5x-x2 and y=x.

Q: 22. Find the area of the shaded region for the function 4e* y = 1+e23 2x

A: The area of shaded region is given by the integral ∫x=ax=b fx dx=∫0ln 34ex1+e2x dx. Let t=ex. This…

Q: Find the area of the shaded region. y 2 x = y' -9 y= 1 x= e - 10 -8 - 6 -4 -2 4 Hy = -1 -2 2.

A: To find the area between the two curves f(y)=x=ey and g(y)=x=y2-9 Area between curves:…

Q: 17. Find the area enclosed by the x-axis and the curve y = -x² +9 32 s.u. а. 3 b. 18 s.u. с. 36 s.u.…

A: Find the area enclosed by the x-axis and the curve y= -x2+9

Q: Ex amine the extreme voalues of the function T lx,y)= x²+ xy+y-6x+ 2 ○くメ<5,-35びかロ。 over the region…

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Q: Find the area of the shaded region below. YA y A x = y² – 4y (-3, 3) – x = 2y – y? Area =

A: Here we have to find the area of the shaded region.

Q: Find the area under the curve y-4x x=D1 and x-D4 O A) NONE OF THESE O B) I DONT KNOW C) 56/3 OD) 9/3

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Q: 1 Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

A: Solution: Here is a helpful picture of the given curves/boundaries alongwith the desired area…

Q: The area between the curves y = 2 – x² and y = x² is given by: • s' (2 – æ²) – (x²) dæ - O si(2²) –…

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Q: 10) Find ff, (x + y) dA where R is the region in the first quadrant bounded by x2 + y2 = 4, y = x…

A: x2+y2= 4 is a eqn of a circle having center at (0, 0) and radius is 4y = x is the eqn of a straight…

Q: Find the area of the shaded region. y 20 (1, 7e) 15 y = 7e 10 5 y = 7xe -1.0 -0.5 0.5 1.0 1.5 2.0

A: This question is related to definite integration, we will solve it using given information

Q: Find the area of the region enclosed by the curve y=e¬5x and the lines y=1 and x=2. .e-10 + 으 10 10…

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Q: Find the area of the shaded region. y 3- x = y - 2 y = 1 x= e X -3 -1 (1 2 3 4 y = -1 -2

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Q: 9- The graph of the function y = x^3 What is the area of the region bounded by the lines y = 0, y =…

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Q: Find the area of the shaded region. У 3 x = y - 2 y = 1 x = ey -3 -1 y = -1 -3 3. 2. 2. 2.

A: To find the area of the shaded region which is bounded by the below functions.

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.