Find the area of the shaded region of the graph of r=1+sin (0)

Q: Sketch the region whose area is given by the definite integral. 36- х2 dx -6-

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Q: Find the area under the curve f(x) = 2x* from x = - 3 to x = 2. Area %3D

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Q: What is the area under the curve f(x) = sinx over the interval [0, pi/2]

A: First:                  Let's draw the graph of the curve f(x)=sin x  over the interval: [0, π2]…

Q: Find the area of the region between the curves y = sin(x), y = sin(2x), x = 0, and x = t/2. Area…

A: Given curve is : y=sinx   .......(1) y=sin2x   ......(2) To find the area of region between curve…

Q: Find the area A of the region that is bounded between the curve f(x) = -2 sin () and the curve g(x)…

A: Given that we have to find the area of the region that is bounded between the curve f(x)=-2sinx4,…

Q: Find the area of the region that lies inside both curves

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Q: Estimate the area under the graph of f(x) = 10 cos(x) from x = 0 to x = π/2 using four approximating…

A: Given that f(x) = 10cos(x)To find the area under the graph of f(x) from x = 0 to x = ?/2 using four…

Q: Evaluate the definite integral.

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Q: Estimate the area under the graph of x) - 5 cos(x) from xO to xR/2 using four approximating…

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Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: Find the area between the curve f(x) =sinx and g(x) = cosx over the interval x=-2 and x=5

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Q: ) Find the area bounded by Y,=cos(x) Y,= sin(x) X-0 and X-IT/2 graph it and show

A: Find the point of intersection of 2 curves.

Q: . Find the area of region between two functions fix)=sinx, g(x)-cos2x,-끌sxs을 %3D

A: The area between two curves A=∫abf(x)-gxdx sinx=cos2xsinx=1-2sin2x2sin2x+sinx-1=0sinx=-1±1+84=-1,…

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

Q: Use trigonometric techniques of integration to evaluate | tan12x sec"x dx' %3D tan15x tan13x + C II

A: To evaluate the given integral use the substitution u = tan x  and the following formula.

Q: area bounded by the curve and perimeter when r^2=sin theta +cos theta

A: We used Octave to plot the above curve. And the code is:  theta=linspace(0,2*pi,1000);…

Q: Find the area under 3 sin(x) and above y = 3 cos(x) for 0 < x < T. that this area may not be defined…

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Q: Find integral.

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Q: 3. Using left and right endpoints give two area approximations for f(x) = sin(x) using four…

A: Lets calculate this on interval x = 0 to x = π  divide this interval in four rectangles,  so,  h =…

Q: Find the trigonometric integral ∫ tan2 x /sec3 x   dx

A: We have to integrate ∫tan2xsec3xdx We will put tanx=sinxcosx and secx=1cosx Given integral can be…

Q: Find the area of the region bounded by the graph of f(x)=sin x and the​ x-axis on the interval…

A: Formula used:∫sinxdx=-cosx+C   , C is the constant of integration

Q: Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) = sin…

A: Solution -  Given function is - f(x) = sinxWe have to calculate the area enclosed by f(x) from x =…

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: In the diagram below, the region between the graphs of y=2 sin¬x and y=rx, in the first quadrant, is…

A: Finding the area of the shaded region

Q: The area between the curves y =2 cos (x) + 4 and y = 2 – 2 cos (x) on the interval [0, 1] is: 27 3 3…

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Q: Estimate the integral cos () dx using four rectangles and midpoints. Round your final answer to four…

A: v Here use the mid-point rule for using four rectangles.   The integral is given as: ∫0πcosx2dx

Q: approximating

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Q: What is the area between the graphs of the functions f (x) = 5 sin x and g (x) = e x − 3, between x…

A: Graph of the given system is:

Q: Find the area bounded by y = sin²(x) and y = sin³ (x) from< xS n.

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Q: Find the area of the shaded region of the graph of r=1+sin(0)

A: Consider the given function r=1+sinθ

Q: Find the area bounded by y = sin²(x) and y = sin5(x) from 0 < x<

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Q: Find the area under the curve 3 over the interval [3, 8]. y = (4x + 2)² Enter the exact answer. area…

A: y = 34x+22,interval : 3, 8

Q: 30. glx) sin x. [0. 7| 6 rectangles

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Q: Find the area of the shaded region. 18- f(x) = 8x + 2x - x°, g(x) = 0 -4 -18-

A: We have the following equation

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

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Q: The region bounded by f(x) = tan x and the x-axis on the interval [0, 7/2) is revolved about the…

A: Volumes of Solids of Revolution: - Revolving the region bordered by y = f(x) and the x-axis on the…

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: Find the area enclosed by the curve r = 2 sin(0) + 3 sin(90).

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Q: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: Find the area under y = 3 cos(x) and above y = 3 sin(x) for T < x < 2n. (Note that this area may not…

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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 under the graph of f(x)= sin' 2x cos 2x on the interval [0, 4).

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Q: Find the total areas of the shaded regions

A: To find the area of the shaded region by the given curve in the figure. Solution: The given curve is…

Q: Use trigonometric techniques of integration to evaluate tan12x sec x dx tan15x tan13x + C

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Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

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Q: Find the area under the curve y = over the interval [4, 7]. (4x + 3)2 Enter the exact answer. area =

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Q: Find the half of the area that lies inside r =1+ sin 0 and outside r = 3 sin 0 %3D

A: Consider the given curves r=1+sinθr=3 sinθ First, find the point of intersection of the curves.…

Q: 5. Find the area of the region between the functions y= secx and y = tan x from x = 0 to x=- 2

A: The given curves are, y=secxy=tanx The limits are x=0 to x=π2. Then, the area is, I=∫0π2secx-tanxdx…

Q: Estimate the area under the graph of f(x) = 3 cos(x) from x 0 to x = 7/2 using four approximating…

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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.