Find the area under the curve f(x) =x+3x+7, above the X axis from x=4 to x=6.

Q: Compute the area bounded by the curve y = 3x - x2, the x-axis and the ordinates x = 2; x = 4.

A: We need to evaluate the area bounded by the following curve : C1 : y = 3x-x2 C2 : x -axis C3  : x =…

Q: Find the area bounded by the curve x^2 + 4y - 8 = 0, the x - axis, and the lines x = 3 and = 5

A:

Q: Find the area between the curve y = 6x – 2x and the x-axis between x 1, and x = 3. ||

A:

Q: Find the area between f(x)=x²-7 and the x-axis from x = 0 and x = 6. ...

A:

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 curves x² and 3x – 2

A:

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

A: The given curves are y=-x and y=2x-x2.

Q: Find the area of the curve y = x° – 2x – 3 between x =- 1 to x = 3.

A:

Q: the area bounded by the curves y=2-x2 and y=x2 is

A:

Q: Find the area under the curve y = 3x 2 from = 1 to x = 2 .

A: We have to find the area of the given curve.

Q: Find the area under the curve from x = 0 to x = 1 of y = (x 4 + x)5 (4x 3 + 1).

A:

Q: find the area between f(x)=x2 +16 and the x-axisn from x=0 to x=8

A: To determine the area between the curve and x-axis.

Q: Calculate the area enclosed between the x-axis and the curve y = x2 - 1 between x = -2 and x = 2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area between the curve  y = x2 + 3x + 2  and the x-axis from  x = −1 to x = 1.

A: We have to find the area between the curve y=x2+3x+2 and the x-axis from x=-1 to x=1.

Q: Find the total area bounded by the x-axis and the curve f(x) = x2 + 3x - 4 over the interval [0, 4]…

A: The given curve is,

Q: Find the area of the region bounded by y = xInx and the x-axis between x=1 and x = e

A: Using formula of Area Under The Curve.

Q: Use integration by substitution to find the area under the curve                            y = 1 /…

A:

Q: Find the area bounded by x2- 6x +y = 0, x² - 2x - y = 0. and the x-axis.

A: We have given two curves;

Q: Find the area between two curves f(x) = x² + 3x and g(x) = 6x.

A: The region bounded between the curves fx=x2+3x and gx=6x

Q: 2. Find the area in the second quadrant bounded by the curve y = x' +4x² –x-4 and the x- axis.

A: To find: The area in the second quadrant bounded by the curve. Given: The equation of the curve is…

Q: Find the area bounded by the line f(x)=2x+2, the curve G(x)=X^2-6X +9 and the two vertical lines X=1…

A: Given:       fx=2x+2        gx=x2-6x+9        x=1,x=5 Area bounded by line and curve is:…

Q: Find the area bounded by the curve x=y²+2y and the line x=8.

A:

Q: Find the area bounded by the curve y=11+5x+x^2 and x-axis from x=−3 to x=−1

A:

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

A:

Q: Find the area between the curve f(x)=x^3−110 and the​ x-axis from x=1 to x=3.

A:

Q: Find the area bounded by f(x) = 3x - 4 and y = 0 for 0 Sxs1.

A: Given: f(x)=3x2-4  ,y=0

Q: Find the area under the curve between x-2 and x=-1 for the curve f(x)=(7 – x²)d

A:

Q: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A:

Q: find the area bounded by the curve y=4x-x² and y=0 from x=0 to x=4

A: Topic = Area

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=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 under the curve f(x)=6 , bounded by the x-axis,x=1 and x=3

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: Find the area between the curve f(x) = x² +12 and the x-axis from x = 3 to x = 6. ...

A:

Q: Find the area of the region between the curve y = 21-x and the interval -1≤ x ≤ 1 of the x-axis.

A: Given: y=21-x, -1,1

Q: 2. Find the area bounded by the curve y = x³ – 3x2 from x = 0 to x = 2. -

A:

Q: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

A: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

Q: Approximate the area under the curve of f (x) = x² +3 from 0 to 4 using the Midpoint Rule with n =…

A:

Q: Find the exact area below the curve y = x°(1 – x) and above the x-ax is. %3D

A: y=x31-x Diagrammatic representation of the required area is,

Q: The area enclosed between the x-axis and the curve y=x2 between x=1 and x=2 is:

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 the area of the region between the curve y = 2x/(1 + x2) and the interval -2<= x <=2 of…

A: Find the area bounded by curves

Q: Find the area bounded by y=-17(x2 - x - 12) and the x-axis. Answer in two decimal places.

A:

Q: Find the area between the curves. y = x2 - 9x + 4 and y = x² + 6 from x = 0 to x = 6

A:

Q: Find the area above the x-axis bounded by the function f(x) = -x2 + 2x + 3 and the x-axis.

A: Given that, f(x) = -x2 + 2x + 3 Points of intersection of f(x) with the x-axis are obtained when:…

Q: find the area between the curves: f(x) = x2  + 1,   g(x) = 3 - x   on the interval [0,3]

A:

Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

A:

Q: . Find the area between the curve f(x) = √x and g(x) = x³.

A:

Q: Find the area bounded by the curve y=10+4x+x^2 and x-axis from x=-3 to x=-1.

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.