Find the areas enclosed by the following curves: (d) x = y² – 1 and x = lyl/1- y2

Q: Find the surface area generated by revolving the portion of the curve y=x^2+1 between x=1 and x=2…

A: Given that, Curve, y=x2+1   We have to find the Surface Area Generated by revolving the portion of…

Q: Find the surface area of revolution about the y-axis of y = 3 – 3x over the interval 0 < x <1

A: Given

Q: Find the area of the surface generated by revolving the semicircle y = √1 − x about the x-axis over…

A: Given that, y=1-x. dydx=121-x-12·-1=-121-x 1+dydx2=1+-121-x2=1+141-x=1+14-4x=4-4x+14-4x=5-4x4-4x

Q: Find the area of the surface formed by revolving the graph of f (x) = x2 on the interval [0,√2]…

A:

Q: Find the surface area of revolution about the x-axis of y = 3x + 4 over the interval 1 < x < 2

A: Answer

Q: Calculate the area of the surface generated when the curve, y = Vx is revolved on the interval [1<…

A: y=x3then x=y3 area of the surface=∫12xddy=∫12y3dy=y4412

Q: Sketch the region enclosed by the given curves and find its area. y = v2x, y = a², 0< x < 6

A: The region is sketch is below:

Q: Find the area of the surface formed by revolving the graph of y = 2e−x on the interval [0, ∞) about…

A: Consider The infinite curve

Q: Sketch the region enclosed by the curves and find its area. 1 x = 0, y = 1, y = e x = - NOTE: Enter…

A: The given curves are: x=1y, x=0, y=1, y=e. The curve x=1y can also be written as y=1x.

Q: Q3/A/Find the surface area generated by rotating the curve y = cos h(x) about x axis for 0≤x≤1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: f(x) = x³, with 0 < x < 1

A: We know, the surface area of the solid that is obtained by rotating the graph of y=f(x) about the…

Q: Find the volume of the solid formed when the area of the region bounded by the curves x2- 3y=8 and…

A:

Q: Find the surface area of revolution about the y-axis of y=6x+3 over the interval 0 ≤ x ≤ 3

A:

Q: 1(b) Find the surface area generated by revolving the portion of the curve y x2 + 1 between x=0 and…

A:

Q: Find the area of the surface generated by revolving the curve a. y = V1+ e* between x = 0 and x = 1…

A:

Q: Find the surface area of revolution about the x-axis of y = 7x +7 over the interval 2 <x < 3

A: Given function,     y=f(x)=7x+7, 2≤x≤3f'(x)=dydx=7Here lower limit is 2 and upper limit is 3

Q: Q5/ Find the area of the surface generated by revolving y = where 0 <x <2, about the X-axis.

A: Given that the area of the surface generated by revolving y=x39 where 0≤x≤2 about x-axis.

Q: Find the area of the surface generated by revolving the curve a. y = V1+ e* between x = 0 O and x =…

A:

Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 0≤x≤1

A:

Q: Find the surface area of revolution about the x-axis of y 4x +7 over the interval 0 < r<3

A:

Q: Q4:B/ Find the area of the surface generated by rotating the curve y = e", 0 < x<1, about the…

A:

Q: Find the area of the surface generated when the given curve is revolved about the given axis.y=8x-4…

A: Here we find the area of surface generated when the given curve is revolved about the y-axis. The…

Q: Sketch the region enclosed by the curves and find its area. 1 ¤ = 0, y = 1, y= e³ x = - NOTE: Enter…

A:

Q: Find the surface area of revolution about the x-axis of y = 2x + 7 over the interval 0 <x <1

A:

Q: Evaluate (x+ y) dx +xy dy, where Cis the positively-oriented boundary of the region bounded by the…

A:

Q: Find the surface area of the solid generated by rotating the curve y = x² about the y-axis over the…

A:

Q: Find the surface area generated by rotating the curve f(x) = 6 – 2x, 1 < x < 3, about the x-axis.

A: We first find the derivative of the given function

Q: Sketch the region enclosed by the given curves andfind its area.   y - cos πx    , y=4x2- 1

A: The given curves are y=cosπx   and  y=4x2-1. Sketch the region enclosed by the above curves as shown…

Q: Sketch the region enclosed by the curves and find its area. 2 x = 0, y = 1, y = e? X = -

A:

Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 2≤x≤5

A:

Q: Sketch the region enclosed by the curves and find its area. 1 Y = V1 – 9x2' y = 2

A:

Q: Find the surface area obtained by revolving the parabolic arc y2=x from (0, 0) to (9, 3) about the…

A:

Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

A:

Q: Calculate the surface area if the curve y = 3sqrt(x) is rotated about the x-axis.

A:

Q: f(x) = x², with 0< y < 4

A:

Q: Evaluate 2e* +y dydx where Ris the semicircular region bounded by the x-axis and the curve y = V1 –…

A:

Q: Find the surface area of revolution about the x-axis of y = 3x + 2 over the interval 0 < z <1

A:

Q: Find the surface area of revolution about the x-axis of y 7x + 7 over the interval 0 < a < 3

A:

Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 V1- NOTE: Enter the exact…

A:

Q: Find the surface area of revolution about the x-axis of y = 5 sin(4x) c

A:

Q: Find the surface area of revolution about the x-axis of y 6x + 3 over the interval 2 < x < 5

A: In the question the curve given is - y=f(x)=6x+3 , 2≤x≤5 We need to find Surface area of revolution…

Q: D Find the area of the surface generated by revolving the region bounded by, 1 1 <x < 5 4 8x2 about…

A: In the question we have to find area of the given function.

Q: Sketch the region enclosed by the curves and find its area. y = |x – 2|, x – 5y + 10 = 0

A:

Q: Find the surface area of revolution about the y-axis of y = 5x + 1 over the interval 0 < x < 3

A:

Q: Find the surface area of revolution about the x-axis of y = 2x + 6 over the interval 2 < x < 5

A:

Q: Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis from…

A: Given: fx=sinx0≤x≤π2 It is required to find the area of surface of the curve when it is revolved…

Q: Find the surface area of the curve f (x) = x over [1,2| rotated .3 3 about the – axis -

A: The revolution of the curve y = f(x) around the x-axis is: S=2π∫abf(x)(f'(x))2+1dx

Q: . Find the area of the region enclosed by the loop of the curve x = 1 – t², y = t – t³ at a pol

A: Solution: The objective is to find the area of the region enclosed by the loop of the curve x=1-t2…