Find the area of the loop of the curve y2=x3 (1-x)6. Show complete solution of points of intersection, your graph with the strip and soln of area using definite integrals.

Q: Find the area bounded by the curve y=4x-x² and the lines x=-2 and y=4.

A: See below

Q: Find the area of the region bounded by the parabola y=5x^2, the tangent line to the parabola is at…

A:

Q: 6. Find the area bounded by the curve 2y² + 4x + y = 0 and the line y = 2x.

A:

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A:

Q: Find the area between the curve y=x^3 and its tangent through (1,1)

A: The slope of the tangent is given by y' at (x,y)=(1,1) y'=3x2At x=1y'=3 Equation of tangent line is…

Q: Estimate the area between the curve y = x^2 - 2x + 5 and the x-axis between x = 0 and x = 3 using 6…

A: Given, y=x2-2x+5 Here, a=0, b=3 and n=6 Therefore, ∆x=b-an3-06=12=0.5 Therefore the intervals are,…

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.

A: so we have and the other function is

Q: Find the area between the two curves on [2,3]. y = ex y = (1/x)

A:

Q: Find the length of the curve y = arcsin e* fromx = 0 to x = In?. Show complete solution of points of…

A:

Q: Find the area bounded by the curve y^2 = 4x and the line 2x + y = 4.

A: Given curves are  y2=4x, 2x+y=4 The region bounded by the above curves  is the yellow colored region…

Q: Find the area between the curve y = 4 – x² and the line y = -x + 2.

A:

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct and…

A:

Q: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0

A: To find the area of region bounded by the given curves.

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y =…

A: x-y3=0  &  x-y=0⇒y3=x  &  y=x⇒y=x13  &  y=x Now the diagrammatic representation of the…

Q: Find the area under the curve y = 5xe- for x > 4. area =|| %3D

A: Explanation of the solution is given below...

Q: Find the area between the curve y = x² + 7x + 12 and the x-axis from x = -3 to x = -1. Step 1 Notice…

A:

Q: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: Find the area between x-axis and the curve defined by   y=2·x2−6·x on the interval [0‍,4].

A:

Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A: to find:- surface area of revolution about x axis.

Q: FInd the area bounded by the give curves y=6x2-8x-2 and y= 3x2+4x-11

A:

Q: Find the area bounded by the loop of the curve y² = 4x²-x*

A: The given equation of the curve is: This can also be written as: The graph of this curve is:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A: The equation of the parabola is given by y = 4x2.Differentiate y = 4x2 with respect to x as follows.

Q: What is the area bounded by the curve y^2 = x and the line x - 4 = 0?

A: We have to determine area of bounded

Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

Q: find the area of the region bounded by the curve y^2=x+1 , both by the x and y axes and the line x=8

A: Using Reimann sums, the area of the region R is given by Sn=∑k=1n∆Ak. This is simply the sum of…

Q: Find the area above the curve y=lnx in the lower half-plane between x=0 and x=1.

A:

Q: Find the area between the curves y = e 1. = y = 2.3x + 1 from x = 0 to x = Area -0.4x and

A:

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: Find the area between the curve y = 9 − (x/2)^2 and the line y = 6 − x.

A:

Q: Find the area between the curve x = y2 and the line x = y + 2 Solution : * with respect to x:

A: Given curves x=y2. . . . 1x=y+2. . . . .2 Equating (1) and (2) y2=y+2y2-y-2=0y-2y+1=0y=2,-1

Q: How can I find the area between the curves?  x=y2-1, x=1-y2

A:

Q: Find the area bounded by the curve y=x3. -x2+3x and the line y=x. 16 4

A:

Q: Find the area between the curves: y=x^3−10x^2+21xx and y=−x^3+10x^2−21x

A:

Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

A:

Q: Find the area bounded by the curve y= 2x-3/x2+4, the coordinate axes and the minimum ordinate. Show…

A:

Q: Find The Area Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

A:

Q: Find the area between x-axis and the curve defined by   y = 2·x2 − 6·x on the interval [0,4].

A: Given curve: y=2x2-6x We need to find the area between x-axis and the curve on the interval 0,4

Q: Find area bounded by the circle x^2+y^2=25, the y-axis and the parabola y=6x-x^2 using iterated…

A: Given : Circle : x2 + y2 = 25, Parabola : y = 6x - x2   To find : Area bounded by the given curves…

Q: Find the area of the region bounded by the parabola y = -x² + 4x - 3 and | its tangent lines at the…

A: We have to find the area of the region.

Q: Find the area bounded by y2 = 4a(y - x), y2 = 2a(x + 2y – 3a) and the x-axis. Show complete solution…

A: To find the area:

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.  show full solution

A:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A:

Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

A:

Q: Find area of the region under the curve y=8−3x^2 and above the x-axis

A: First we find where y=8−3x2 cuts x axis. We set y=0 and solve for x

Q: Find the area bounded by the curve 4y² + 16x – 15 = 0 and the linex = -1. %3D

A:

Q: Find the area between the curves. 3x 3x x-0, x-D4, y3D2e" y-e

A:

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.  Show full complete solution.

A: Given : Curve : y²= 4x              and line  2x+y=4 To find : Area between the curve and line

Q: Find the area of the region bounded by the curve y=1--x2 and the x-axis. 9

A:

Q: Find the area bounded by the curves y=x4-2x2 and y=-x2+4 at an [-1, 1].

A: The region bounded by the curves y=x4-2x2, y=-x2+4 in [-1,1] is:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.