Find the area between the curve y = tan x and the x-axis from x = -pai/4 to x = pai/3.

Q: Find the exact area between f(x) = 2x and g(x) = 15 – x from the vertical axis to their point of…

A:

Q: Find the area under the curve below from x = 1 to x = 4. y = 5x + (3/x2)

A: We have to solve the area

Q: 29) Find the area bounded by the curves y= In x, y = 2 In x and line x-e in the first quadrant.

A: I have given the answer in the next step. Hope you understand that

Q: Find the exact value of the area between the graphs of e for 0 < x < 1.9. y = 1 – x and y area =

A: Recall: Area=∫abf(x)-g(x)dx We have, a=0, b=1.9, f(x)=1-x, g(x)=ex

Q: Approximate the area under the curve graphed below from x = 1 to x = 6 using a Left Endpoint…

A: Given:

Q: Approximate the area under the curve y=x^2 from x=1 to x=3 using a Right Endpoint approximation with…

A:

Q: Find the area under the curve y=f(x)=x^3 from x=1 to x=3 using inscribed and circumscribed…

A:

Q: use a definite intergal to find the area under the curve between the give x-values. f(x)=2ex from…

A: Given data: f(x)=2ex from x=0 to x=ln4

Q: Approximate the area under the curve y=x^2 from x=0 to x=2 using a Right Endpoint approximation with…

A:

Q: What is the area under the curve y = x° and above the x-axis between x = 1 and x = 3? What is the…

A: We have to use integration here.

Q: Find the area between the given curves: f(x) = sinx g(x) = cosx on the interval (0, π)

A: Sketch the region bounded by the curves fx=sinx  and  gx=cosx   on 0, π as shown below.

Q: Find the survace area of revolution about the x-axis of y= 4sin(2x) over the interval x is greater…

A: Given: The curve y=4sin2x for 0≤x≤π2 To find: Surface area of revolution of given curve about…

Q: Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.

A: The given two curves are,

Q: Find the area enclosed by the given curves. 11) Find the area between the curve y = 6x/(1 + x2) and…

A:

Q: sin(z)

A:

Q: What is the area under the curve represented by the function f(x)=x√x?

A: Topic = Application of integration

Q: Find the area under the given curve over the indicated interval. y =x +6x+ 1; [3, 5]

A: To find area under the curve we use definite integrals.

Q: Find the area between the curves y = cos(x) and y = sin(x)  from x = -3π/4 to x = π/4. Draw the…

A: To find the area between the curves.

Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

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 between the curve y=2x+4x-6 and the x-axis from x =-2 to x= 3.

A:

Q: Find the area between the curve and the x axis over the indicated interval. y=8/x; [1,7]

A: We will use integration to find area under the curve

Q: Approximate the area under the curve y=x^2 from x=0 to x=3 using a Right Endpoint approximation with…

A:

Q: Find the area between the curve y = x2 + 10x + 16 and the x-axis from x = −2 to x = 1.

A: We have limits of curve from x=-2 to x=1

Q: Find the area under y = 2 sin(x) + 2 cos(x) and above the x-axis from x = 0 to x = Tt/2. Leave your…

A: The given function is,

Q: Use a definite integral to find the area of the region between the curve y = 17x and the xX-axis on…

A: Area is the double integral with respect to y and x. It is known that at x-axis that is y=0. We have…

Q: Approximate the area under the curve y = x² from x = 1 to x = 3 using a Right Endpoint approximation…

A:

Q: The question is "What is the area under the curve at the right?" How and what are the steps to…

A:

Q: Approximate the area under the curve y=x^2 from x=3  to x=6 using a Right Endpoint approximation…

A: Given: y=x2

Q: Find the area under the graph of y=sin3xcos2x integrate from 0 to pi/4

A:

Q: Find the area between the graphs of f(x)=sinx and g(x)=cosx for <x< 4

A: Graph of area from π4to5π4 is shown below÷ Red curve = sin(x) Blue cuve = cos(x)

Q: Compute the area bounded by curve y = ln x the x - axis and straight line x=e.

A: Let us consider the curve y=f(x) and y=g(x) in the interval a≤x≤b then the area under the curve is…

Q: Find the area between y = ln x and the x-axis from x = 1 to x = 3.

A:

Q: Find the area bounded by y = 0.5(x- 2)² – 1 and the X-axis from x-3 to x-5. Show the sketch with…

A: y= 0.5(x-2)2-10 =0.5(x-2)2-11 = 0.5 (x-2)22 = (x-2)2x - 2 = ± 2x =2+2    x~ 3.414orx =2-2x ~ 0.586

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 curve and the x-axis over the indicated interval. y = 25 - x2; [-5, 5|

A:

Q: Find the area between the curve y = tan x and the x-axis from x = -π/4 to x = π/3

A: y=tanx from x=-π4 to x=π3. The graph is,

Q: Find the area bounded by the curve f(x) = -x² + 7 and the x-axis. Give your answer correct to two…

A: We have to find Area bounded by the given curve and x-axis.

Q: 14. y= sin x with n 6. Round to the ten-thousandths place. on

A: The objective is to compute the area under the curve y=sinx on π4,π using 6 subintervals.

Q: Approximate the area under the curve y = x from x = 1 to x = 3 using a Right Endpoint approximation…

A:

Q: Find the area the region lying between the x axis and the curve y=(ln(8x)-1)/x2 to the right of the…

A: Given curve is y=ln(8x)-1x2 Since region lying between x-axis and the curve to the right of the line…

Q: Evaluate the integral.  integral  cot  5 x  csc 4  x  dx

A: We have to evaluate the integral: ∫cot5 x cosec4 x dx Rewriting the integral, ∫cot5 x cosec4 x…

Q: Find the area between the curve  y = x2 + 10x + 16  and the x-axis from  x = −2 to x = 1.  (Give…

A: To find the area between the curve y=x2+10x+16 and the x-axis from x=-2 to x=1. This is given by…

Q: 3. Find the area between the curve y = 2sinx cos x and the x-axis within the interval [0,2π].

A:

Q: 1. Approximate the area under the curve y = sin(x) from 0 to - using 8 approximating rectangles of…

A:

Q: Approximate the area under the curve y=x^2 from x=1 to x=4 using a Right Endpoint approximation with…

A:

Q: Set up the definite integral required to find the area of the region between the graph of y = – 23x…

A:

Q: Approximate the area under the curve y = x from x= x³ with 6 subdivisions. = 2 to 5 using a Right…

A: The curve y=x3 from x=2 to x=5 we have to find the area under the curve using Right Endpoint…

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.