13. Find the area of the region enclosed by the following curves in the ways: (i) integrating with respect to x (ii) integrating with respect to y. a. x = y and y = x³ b. y = x² and x = y?

Q: 15. Sketch the region enclosed by the lines x = 3 and y = 1 and the curve xy = 9, and find its area.

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

Q: Find the area of the region enclosed by the curves y = x and y = 4x by integrating with respect to…

A: The given curves are: y=x2  and   y=4x The region enclosed by these two curves is given as:

Q: 3. Find the area of the region in the first quadrant that is bounded above by y = vx and below the…

A: Solution

Q: 12. Find the area of the region enclosed between the curves defined by the equations y = √(x + 2), y…

A: We have to evaluate the area of the region bounded by the curve y=x+2 and the line y=x using the…

Q: 8. Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and…

A:

Q: 1. Find the area bounded by the curve y In x and the %3D lines y = 0 and x = e.

A: Given curve is: y=lnx and the line y=0 and x=e Area of bounded regions: Let y=f(x) be a continuous…

Q: Sketch the region between y = sin x and y = cos x over the interval and find its area: [0, π]

A: Consider the given function as y=sinx and y=cosx

Q: (b) Find the area of the region by integrating with respect to y.

A:

Q: Find the Area between the curve y = sin(x) and y = cos(x) and the lin es x = 0 %3D and x = n?

A:

Q: 1. Find the area of the region bounded above by the curve y = 2e-* + x, below by the curve y = , on…

A: We have to find out the area of the region bounded above by the curve   y = 2e-x + x , below by the…

Q: b. Find the area bounded by the curve y = Vxe-Vx and the x-axis from x = 0 to x = 4. (45 Ivarks)

A:

Q: Find the area between y = ex and y = e2x over [0, 1].

A:

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x, y=0, x=TT/4, x= TT/2 ? ans/…

A: The curve is given as y=cos2x The objective is to find the area of the shaded part.

Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

A: Given: curves y=x^2+10x , y=2x+9 We have to find the area between the curves

Q: 4) Find the area of the region bounded by the given curves. a) y = sin(x) cos(x) and y = sin(x) , 0…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Calculate the area contained between the curve y = cos x, π<x< , and the line y =

A: Given:-y=cosx, -π&lt;x&lt;πy=1/2

Q: 1. Find the area between the curves of y = x2 +1 and y = x +7 from x = -2 to x = 3. Round to two…

A: Topic-application of integration

Q: 4. a) calculate the area of the area bounded by the Curves TI y=Sin 2x and y sin 2x, OSX<

A:

Q: Find the area of the region bounded above by y = sin(x) and below by y = cos(x 2 1.5 4 0.5+ X

A: Using horizontal /vertical strip

Q: 2. Find the total area of the region between the curves y = sinx and y = cosx for 0<xs 37 2

A:

Q: Find the area enclosed by the curves y=sin(x), y=cos⁡(x), and the two vertical lines x=0 and x=π/2

A:

Q: 1. Find the area bounded between the curves: y = x°, x = 1, and y -8

A:

Q: 4. Set up the integral for the area of the surface obtained by rotating the curve y = e-x -1 < x< 1.…

A: Given: The area of the surface obtained by rotating the curve y=e-x2  and -1≤x≤1 we have to…

Q: = Set up the definite integral required to find the area of the region between the graph of y y = 2x…

A:

Q: 15. Find the area of the region enclosed by the curve x = y³ – y' and the line x = 2y. (Hint: Need…

A: We are asked to find the area of the region

Q: 4. Find the area enclosed by: a. y= sin(x) and y= cos(x), x 0, x =" and the y-axis. 2

A:

Q: 2. Find the area of the indiconted region. Between y=x3 and y=1 For x in El,ņ I for x in El,]

A:

Q: Set up a definite integral to find the perimeter of the region bounded by y = ex, y = e-x, and x =…

A: Given curves are: y=ex;y=e-x The point of intersection of these curves is obtained when:…

Q: Find the area enclosed by the given curves. y = x3, y = 4x O 4 O 2 8 O 16

A: topic - area enclosed by curves

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x y=0, x=TT/4, x= TT/2 ? ans/ 1/2

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

Q: 1) Find the area of the region bounded by the curve y=3x•e-2* and the x-axis, for x>0. i) Rou imal

A:

Q: 1. Sketch the region enclosed by the given curves and find its area. y = x², y = x*

A: Answer

Q: Find the area bounded by the given curves. y = 2x - x2, y = 2x- 4 32 O A. w/ 3 37 OB. 3 31 OC. 3

A: The objective is to find the area bounded by the given curves

Q: 4/Find the area of the region enclosed between the curves y=0, x=TT/4, x= TT/2 ? ans/ 1/2

A: The curves given to us is  y=cos2x,y=0x=π4,x=π2

Q: 5. Use the concept of the definite integral to find the area of the region under the graph of y =…

A: we have to use the concept of the definite integral to find the area of the region under the graph…

Q: problem in photo attached

A: Consider the given functions:

Q: 1. Find the area between the curves of y = x² + 1 and y = x + 7 from x = -2 to x = 3. Round to two…

A: (Note: We are entitled to solve only one question at a time) Given: y=x2+1 and y=x+7 x=-2 , x=3. To…

Q: 7. Find the area bounded by x = t2,y = 1– t3,0st<1 and the y-axis

A:

Q: Set up the definite integral required to find the area of the region between the graph of y = 17 – x…

A: We have to find

Q: Calculate the total area between the given curves for 0 < x < ™. f(x) = cos(x), g(x) = 1– cos(x)

A:

Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: Q 3:- Set up an integral that can be used to determine the area of the bounded region by the gra of…

A:

Q: 1, and the x!/4. By writing x as a function of y and integrating Let R be the region bounded by the…

A:

Q: Find the area enclosed by the given curves. y = - 4sin x, y = sin 2x, 0 < x s T 1 8 O 16 O 4

A:

Q: 4 / Find the area of the region enclosed between the curves y%3= cos 2x, y=0, x-TT/4, x- TT/2 ? ans/…

A: we allowed providing one solution at a time. Please upload the rest questions seprately.   Question…

Q: Consider the region between the curves y = 5x and y = r in the first quadrant. a- Set up an integral…

A: We use integration to find area between curve and given line

Q: a) Find the area between the two curves y = 6 – x and y = x² by (i) integrating with respect to x…

A: Given curves: y=6-x and y=x2 To find: The area between the two curves y=6-x and y=x2 by…

Q: B- Find the area under curve y= (e*/x )dx from x=0 to x=4. use midpoint method with n=4

A: By Midpoint Rule:

Q: 1. Find the AREA of the region bounded by y = y=x, and y = 5. Express the answer as an exact value…

A: Please see the explanation below

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.