Find area of the region lying inside the circle r(0) = 3 sin 0 and outside of the %3D cardioid r(8) = 1+ sin 0.

Q: Find the area outside the curver=3+2cose and inside the curve =3-3cose. A B C D M 4 A 2 5A 4 NY 2…

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Q: Find the area of y = sin x, y = sin3 x

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Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: Find the area inside the 'figure eight'r = 1+ cos 20 and outside the circle r = 1.

A: Area inside r = 1 + cos2θ and outside r = 1 is shown by shaded region.

Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

Q: Q/ Let w=F(Xi)) and X= V cose, y=Y Sine Show that (w 2 %3D Y

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Q: Q4) Find the shared area between the two cardlold r=1+sin@ and r%3D1-sin0

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Q: Find y' of cot (xy2) + xy = x².

A: Given query is to find derivative of the expression.

Q: dy/dx=-2x(tany

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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: solve 2 (pedoe tydy +2d₂) ² 2 = {(2²-x²=y²2) (seds tydy + z dz/d2} z

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Q: Evaluate x2 dx Select one: on O(sin (2r- 1) + 2(2 (2ain (r) + sin(2si To (stn(2 1I) 2(2r sin(2sin

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Q: Find and if dy dx² dy dx = 5 sec 0 and y = 5 tane

A: Given: x=5secθy=5tanθ

Q: find area, y=2x , y=3-x2  (0,1)

A: Area is a 2-dimensional quantity which is the measure of amount of space covered by any shape in 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.