3) Which integral expresses the arc length of y = In(cos x) from ×= a | 6 to x = 7 | 4? x =π/6 J sec(x) dx a) r16 S V1+ (In(cos x))² dx b) x16 | (1+ tan(x)) dx c) r16

Q: Evaluate the integral (2x+3y) dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A: To Evaluate: I=∫C(2x+3y)dx+(6x-y)dy along the parabolic arc y=x2 from (0,0) to (1,1).

Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A:

Q: Consider the curve segments: 1 to x = 2 and 3 1 to x = 4. S1: y = x from x = S2: y = Vx from x = Set…

A:

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

A:

Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

A:

Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A:

Q: Evaluate the integral / (2x + 15y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A:

Q: What is the antiderivative of g(x) = 2 cos(x) that contains the point (7, 0)? 4 O 2 sin(x) –V2 O 2…

A:

Q: Which integral computes arc length of f(x) = 5/2 on 0, 1 1 1+ x° dx 0. 1 I V1+x³ dx 0. 1 49 7 1+x'…

A: Given function: fx=x52 on interval [0,1] Differentiate the given function w.r.t "x"…

Q: 20. Which integral gives the arclength of y = 2Vx on the interval from x=0 to x=4? Recall b 2 dy…

A: We use the formula of arc length.

Q: The integral dx is improper for two reasons: The interval [0, co) is infinite and the integrand has…

A:

Q: Consider the curve segments: 1 $1: y = x from x = to x = 4 and 3 1 S2: y = Vxfrom x = -to x = 16.…

A:

Q: The arc-length of the curve y= Vcos(4t) dt, for 0<x<; is given by which of the following 8…

A: We will use the formula for Length of the arc and fundamental theorem of Calculus.

Q: (b) Consider a volume of a solid under the surface z = sin(x³) can be denoted as 4 2 | sin(x³) dx dy…

A: In this question ,we can reverse the order of the integration. Firstly draw the limits of 'x' and…

Q: Integrate f(z) = 6 tan(z²) counterclockwise around the unit circle, using Cauchy's integral theorem…

A:

Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: Consider the curve segments: 1 $1: y = x² from x =to x = 3 and 3 1 52: y = Vx from x =to x = 9. Set…

A:

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: 0; x 0

A:

Q: Evaluate the integral | (6x + 3y)dx + (9x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

A:

Q: Consider the curve segments: 1 S1: y = x from x = to x = 3 and S2: y = Vx from x = 1 -to x = 9. 16…

A: Use formula of length of arc

Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxy dydx

A: We have to integrate the double integral:

Q: Evaluate the integral (8x +12y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A: Topic:- integration

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

A: Solution is below

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Evaluate the integral / (8x + 3y)dx + (18x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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

Q: 3. Find the area of the region that lies inside both curves: r = sin 0,r = cos 0 0.8 0.6 0.4 0.2…

A:

Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A:

Q: Which integral 12 225-x¹+1 2 S√√2-√√225x4+1 dx So 9 is the arclength of the curve y = 5 x³ on the…

A:

Q: Evaluate the integral [(4x + 15y)da + (6x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A:

Q: Evaluate the integral (8x +9y)dx + (3x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: We can observe that x is ranging from 0 to 1. We have the following. So,…

Q: Set up an integral that (if solved) would give the arc-length of the following curve on the given…

A:

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: The curve segment y = x² from x = 1to x = 2may also be expressed as the graph of x = √ y from y = 1…

A: Given any function y=f(x) we can write this function in the form of vector function…

Q: Consider the curve segments: 51: y = x from x =to x = 3 and 1 52: y = Vitrom x =; to x = 9. Set up…

A:

Q: Which integral computes arc length of f(x) = x5/2 on [0, 1]? 1 49 -x' dx 1+ 4 - 1 | V1+ x° dx 1 1+…

A: We have to find the arc length

Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

A:

Q: Evaluate the integral / (4x + 18y)dx + (27x – y)dy along the parabolic arc y = 2? from (0,0) to (1,…

A:

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: Which integral expresses the arc length of y= In(cos x) from x = n / 6 to x = T |4? | sec(x) dx |…

A:

Q: Evaluate the integral (2x+3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A:

Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A:

Q: Consider the curve segments: S1: y = x² from x == to x = 3 and 52: y = √√x from x = to x = 9. Set up…

A:

Q: Evaluate the integral / (8x + 18y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: We have to find value of given Integral along given Curve.

Q: The area of the surface generated by rotating the curve y = 1 = cos(3x), where 0 ≤ x ≤ , about the…

A: Let's find Area of surface,when rotated about x axis.

Q: 7. Find the indefinite integral. 1. dx V9-16x? 4x 1 tar arcsin 3 +C_b. arcsin(9x) +C a. 4 4x c.…

A:

Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

A:

Q: Consider the curve segments: S1: y = r from x = to x = 4 and !! S2: y = Va from x=- to x = 16. Set…

A:

Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

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.