Consider the quarter-circle of radius 1 and right triangles ABE and ACD given in the accompanying figure. Use standard area formu- las to conclude that 1 sin 0 zsin e cos 0 < 2 2 cos 0' y (0, 1) D (1, 0) A|

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: Find the arc length of the catenary y = coshx between x 0 and x = In4.

A: we'll allow providing one solution at a time. Please submit the rest questions separately.   Given:…

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 2 cos(0), y…

A:

Q: Find the area between the curves y = 4 cos(6x),    y = 4 sin(12x),    x = 0,    x = π/12

A: Given,

Q: Use the Fundamental Theorem of Line Integrals to calculate exactly. F-6 sin(ox +)+ sin(6x )j along…

A:

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: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

A:

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

A:

Q: Evaluate the integral ſ sin x dx by the method of geometry.

A:

Q: Let A be a curve defined by the equations 3 x = 3t2 – 4 and y = sin (-nt). Set up (do not evaluate)…

A: Here, the given parametric curve A is: x=3t2-4, y=sin-32πt Now, to find the arc length of A from…

Q: y = 0, y = cos 2x, on the interval li [引 %3D

A:

Q: Find the arc length of the graph of the function y=ln(cosx)y=ln(cosx) over the interval…

A:

Q: Find the arc length of f(x) = In(cos x) on- %3D 4

A:

Q: The arc y=2 sqrt root(x) from x ∈ [4,16] is rotated about the x axis. Find the exact surface area…

A:

Q: Find the area enclosed by the curve whose equation is given below: r = 1- 0.6 sin 0

A: Given curve is r=1−0.6sinθ We have to find the area enclosed by the curve r=1−0.6sinθ Area is given…

Q: Find the length of the curve y = arcsin e* fromx = 0 to x = In?. Show complete solution of points of…

A:

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: This question is about application of integration

Q: Find the arc length of y=In tanh 2 2<x54 Select one: sinh 2 In sinh 4 O None sinh 4 O In sinh 2. 4…

A:

Q: Find the area bounded by the trigonometric curves O2.828 square units 1.414 square units 3.667…

A: To find: To find the area bounded by the trigonometric curves- y=sin x and y=cos x from x=π4 to…

Q: Find the arc length of f(x) = () (x² + 2)z on the interval [0,9] %3D

A: (6) Given function is fx=13x2+232 and interval is 0,9. We have to find the arc length of fx=13x2+232…

Q: Calculate the area of the circle r = 8 sin 0 as an integral in polar coordinates. Be careful to…

A:

Q: Calculate the arc length of y = In (cos(8x)) over the interval [0, . (Use symbolic notation and…

A: we have to find the arc length

Q: With its curve y = cos determine its area under one arch.

A:

Q: 1. f (x) = cosh x on [0, 1] %3|

A:

Q: Compute the arc length of y = ln(x) – (1/8)x² on 1< < 3

A: Arc length:       Arc length is the distance between two points along a section of the curve.  Let…

Q: Find  the Arc length of the graph of y=Ln(cosx) from x=0 to x=π/4

A:

Q: Q: Prove that the arc lenfth af Curve y = log secx from to n- 3 is Use formula Note I+ ( dn.

A: Given: y = log sec x To prove: The arc length of the function y from x = 0 to is .

Q: Ssin (3x)cos (3x) dx 3. Evaluate the trigonometric integral ·

A:

Q: What is the area under the curve y = cosx over the interval [0 ,π/2]?

A: Integrating the equation of curve in the given interval gives the area

Q: The arc length of the curve r= cos 30 with 0<0 < is T V(sin 30)² + (cos 30)² do 0. o" V-9(sin 30)² +…

A: Given that: r=cos3θand  0≤θ≤π

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

A:

Q: Set up an integral to find the arc length of the curve defined by  x = tany  on the intergral 0 ≤ y…

A:

Q: The region is bounded by the graphs of the equations y sin x, y = 0, x=0, and x-A. For the…

A: See this solution in below

Q: Sketch the curve. r=3-sin(0) 1 Find the area that it encloses. 1 2 3 2 + -2 1 2 -2 -1 1 OO 3 -3 -2 2…

A:

Q: Estimate the arc length from point (0,0) to (1,1) on the graph of y = x² using the Composite…

A: arc length  of the curve y=f(x) from x=a to x=b  L=∫abds  where ds=dx2+dy2=1+dydx2dx Integral have…

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

A:

Q: y = sin(x), y = 2x

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: Calculate the arc length of y = x² - In(x) over the interval [1, 10e]. %3D (Use decimal notation.…

A:

Q: sin°(x)cos*(x)dx 2, 4

A:

Q: Find the surface area of revolution about the x-axis of 3 sin(7x) over the interval 0 < z <

A:

Q: Determine the exact arc length, L, of the curve y-ln (sec z) on the interval 0szS/3. L Please make…

A: Given problem:- Determine the exact arc length, L, of the curve y = ln(sec(x)) on the interval [0,…

Q: Calculate the arc length of y = In (cos(4x)) over the interval 0, . (Use symbolic notation and…

A:

Q: A curve is drawn on a sphere of radius "a' and the principal normal at a point P makes an angle 0…

A:

Q: Consider the curve given by f( x ) = 4 cos( 2.5 x) on the interval 0 sxs 2 n. 4 1 -1 -2 -3 -4 1 4 6.…

A:

Q: The arc length of the curve r= cos 30 with 0<0<T is J V (sin 30)² + (cos 30)² d0 T" V-9(sin 30)² +…

A:

Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

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

A: