4 Tt /4 * tan*x sec*x dx

Q: Find the length of the entire perimeter of the region inside 15 sin 0 but outside r = 1.

A: The region is inside r=15sin θ but outside the r = 1

Q: Find the total area between r = 4 sin(0) and r = 7 sin(40). %3D

A: Double integral is used to integrate the function of two variables over two-dimensional region.…

Q: what is the area between the curves: y = 7 cos( pi*x),    y = 12x2 − 3

A: 7cos(πx) and 12x2-3

Q: ((csc(y))2 – csc(y)cot(y)) dy

A:

Q: Find the area of the specified region. Inside the limaçonr=8+2 sin 0

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Q: Find the exact area inside r = 4 sin(0) and above r = 2 csc(0). %3D

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Q: dy 2 y у (4 — у

A:

Q: Find the indicated Trapezoid Rule approximation to the following integral. .3 5 sin 3* dx using n =…

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Q: Find the indicated Trapezoid Rule approximation to the following integral. TC sin dx using n = 6…

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Q: Find the area enclosed by the given curves. y = sin x, y = csc 2 x, < x <

A: The given curves are: y=csc2x, y=sinx and the interval is π3≤x≤π2

Q: X +25 x = 5 tan(0) 'xp

A: Given: - The Indefinite integral is,  ∫x3x2+25dx, where x=5tanθ To find: - The solution of the given…

Q: Find the Area between the curve y = sin(x) and y = cos(x) and the lin es x = 0 %3D and x = n?

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Q: Find the area between the curves y = cos x and y=−sinxfrom 0 to π/2:

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Q: Compute the surface area of the surface generated by revolving one arch of the cycloid c(t) = (10 (t…

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Q: Find the area under one arch of the cycloid. x = 6a(t- sin t), y = 6a(1 – cos t)

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

A: Given information

Q: Evaluate the following integral. 2. | cot 'x csc x dx ot 'x cscx dx 2. cot'x csc ´x dx =

A:

Q: Find the indicated Trapezoid Rule approximation to the following integral.

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Q: Use the Trapezium Rule with four strips to estimate the value of: A xln(x+1)dx. Note that f(0) = 0°…

A:

Q: Find the indicated Trapezoid Rule approximation to the following integral. 2 sin -x dx using n = 6…

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Q: Evaluate the integral * T/4 cosh (tan 0) sec² 0 d0 7/4 TT

A: In this question we have to find the integration.

Q: Take the following integral 4 dx 1 VT

A: We can find the integration as below

Q: Evaluate the integral frever se 2. 2. SS 24 S sinxy ds dx

A: According to the given information it is required to evaluate the given integral:

Q: Use the Substitution Rule to find the following indefiniteintegrals. Check your work by…

A: The given integral is ∫22x+13dx

Q: Show that if k is a positive constant, then the area between the x-axis and one arch of the curve y…

A: y = sin kx cuts the x axis at y=0. Solve for x.

Q: 2 Find the definite integral fo5 tan(x)dx using strips of width for the trapezium rule correct to…

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Q: Find the area between y = x + 11 and y = 3x + 2 between x O and x 2. %3D |3D Enter the exact answer

A: Given:       y=x+11       y=3x+2 over interval 0,2 The area between curves is the area between a…

Q: Find the indicated trapezoid rule approximation to the following integral. 3

A:

Q: Find a limit equal to the area shown. y-sin (21)

A: Given y=sin2x To find the width π2-0n=π2n So now ∑i=1nf0+π2niπ2n Which is,…

Q: Find the area bounded by y = sin(2x), y = cos(4x), x = Tand x = 12 %3D 12 The area is B/3 sq units.…

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Q: nd the area between y = 8 sin x and y = = = 10 cos x over the interval

A: Topic:- application of integration

Q: Determine the area enclosed by the following curves r= 4+ 3 sin 0 #/12 + V3/16

A: Here, we need to determine the area enclosed by the curve r=4+3sinθ. Notice that the curve has…

Q: evaluate using trigonometric substitution. Refer to the table of trigonometric integralsas necessary

A: Let, Then we integrate by substitution

Q: The definite integral /. '(tan2(x) + sec2(x) ]dx when evaluated is equal to AV3 + Br where A, B are…

A:

Q: • S/2 csc²2x√√1+cot 2x dx TT/8

A: The given integral is∫π8π4csc22x1+cot2xdx. The objective is to solve ∫π8π4csc22x1+cot2xdx.

Q: Find the area between the curve y = 1/x7° and the x-axis from x = 1 to co. square units

A: Given: The area between the curve y=1x76 from x=1 to ∞ To find the area of the curve. The formula…

Q: find the area of the circle r=a by integration

A: The diagrammatic representation is,

Q: Use one of the formulas below to find the area under one arch of the cycloid x = t - sin(t), y = 1 -…

A: Given arch of cycloid, x=t-sin(t), y=1-cos(t)

Q: Find the inde finite integral Slox+7)dx= =xP(L

A:

Q: Find the area enclosed by the curves below from x = 0 to x = - y = 45 cos(9x) y = 45 sin(9æ) Area =

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Q: The area enclosed by the circler= = sin 0 is given by 2x esin 0 A = f" Sr dr d0.

A: Given that  The area enclosed by the circle r=sintheta is given

Q: Find the exact area inside r = 6 sin 0 and outside r = 3.

A:

Q: If the area enclosed by the curve x = 5 cos3 t and y 5 sin t (where t E R) is A¨, then what 8. is A?

A:

Q: Evaluate the integral / cot x csc² x dx using the substitution u = cot x. cot° x csc² x dx = +C

A: From the given problem: I=∫cot6xcsc2xdx    .....1 Now using the substitution method to solve the…

Q: Find the area of one leaf of the rose r = sin(15θ). Enter your answer in terms of π, do not use…

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Q: ind c such that the area between the curves y = r- c and y = c -2 is equal to 69. Round your nswer…

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Q: Use Simpson's rule with interval h = 1 to determine the approximate value of V(1 + x³ )dx. Give…

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Q: find Ihe area of ThI Surlace genecated by +Y about -akis; oEXEI

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Q: Find the area under one arch of the trochoid x 70-1 sin(0), y = 7–1 cos(0).

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Q: For the given integral dx sin2x/1+ cotx what is u? note: no space between symbols in your answer

A: