Find the area under y = 2 sin(x) + 2 cos(x) and above the x-axis from x = 0 to x = Tt/2. Leave your answer in its exact form. f(x)dx. If you are using a graphing calculator, verify your answer numerically using FnInt or У y = 2 sin(x) + 2 cos(x) х 2.

Q: /Find the area under the curve y = sin x cos 2x from x=0 to x =-

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral S7 n = 20…

A: we nee to find ∫π4π2ln(tanx)dx,  n=20 a=π4=0.7854,  b=π2=1.5708 ,  y=ln(tanx)…

Q: Find the area bounded by the parabolas x2+y-9=0 and x2-8y=0   (SOLVE BY USING INTEGRAL CALCULUS)

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

A: Given,

Q: Calculate the integral approximation S10 for Si, dx. 1 x5+1 S10 =

A: Let's find integration value by using simpson rule.

Q: How large should we take in order to guarantee that the Trapezoidaland Midpoint Rule approximations…

A: Given

Q: The arc-length of the curve y= Vcos(21) dt , for 0<x<= is given by which of the following integrals?…

A: Here we have to find the arc-length of the given curve .

Q: Evaluate the integral: |x cosh x² dx sinh x +C 2 x sinh x? +C sinh x? +C x² sinh 2x +C

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Q: Find the indicated Midpoint Rule approximation to the following integral. 13 |3x dx using n= 1, 2,…

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Q: Approximate the following integrals using the Trapezoidal rule. r0.35 2 dx x2-4 1. 2. Sfx sin(x) dx…

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Q: In evaluating the indefinite integral / sin x cos x d , the appropriate u – substitution and. the…

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Q: Set up the definite integral required to find the area of the region under the graph of y = – 4x +…

A: From the given lines, y=-4x+22, x=-3, x=3 the bounded region is as shown below; Now take an…

Q: For evaluating the integral x tan-lr dx, we apply integration by parts technique with the…

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Q: 3. x Arctan(x) dx

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Q: . Split the region between the two curves into two smaller regions, then determine the area by…

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Q: Find the value of the definite integrallo 2 cos ( x ) dx given that the antiderivative for the…

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Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2 for 2≤x≤6 if you integrate with…

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Q: Use the tabular method to find the indefinite integral. ∫(1 − x)(e−x + 1) dx

A: We multiply the integrand then integrate each part…

Q: y5 dy; 4 + y*

A: The given integral is ∫y54+y4dy  ...... (1) Substitute u=y2 . This implies  y=u Differentiate u=y2…

Q: 3) a) Use Simpson's rule with n=4. b) Estimate the error in the approximation. -2x dx jedx to…

A: Given integral is ∫06e−2xdx. a We have to approximate the given integral by using Simpson rule.…

Q: [₁ 2x - x² dx

A: To integrate.

Q: x2 – 12 and Set up the definite integral required to find the area of the region between the graph…

A: The x coordinate of the points of intersection of the curves will be the limits. Let, f(x) = y = x2…

Q: evaluate the definity integral  from -10 to 10  (2 - x)dx

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Q: Use Simpson's rule to find the value of the following integral e-3x dx where n=4 0.1

A: By the Simpson's rule, ∫abfxdx≈∆x3fx0+4fx1+2fx2+4fx3+...+4fxn-1 here n is 4, a = 0.1 and b=0.9. Then…

Q: = Set up the definite integral required to find the area of the region between the graph of y y = 2x…

A: The integration formula for ∫xndx=xn+1n+1+C

Q: Evaluate the integral. TC cos(x) sinh(x) dx

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Q: Find the indefinite integral. ∫ cost /(1 + sin t) dt

A: we have to find the value of the given indefinite integral: ∫cost1+sintdt let the given integral be…

Q: 2. +4) dx

A: Given: ∫02x2+4dx

Q: Use Simpson’s Rule with n= 10 to approximate the integral 0 to 1 e x2   dx

A: Given: n=10I=∫01ex2dx

Q: Evaluate the iterated integral. 4 (x + 7)dy dx Exact number, no tolerance. (x + 7)dy dx = i

A: We have definite Integration to solve.

Q: Use Simpson rule' 1/3 Method with (n = 8) to estimate the integral: f(x) : e^(sin 9x), where a = 0 &…

A: Given; f(x) = e^(sin 9x) and n=8 And a=0 , b=10

Q: Set up the definite integral required to find the area of the region between the graph of y = 15x +…

A: here i am giving my handwritten solution.

Q: Find the area under the curve y = sin √x /√x between x = π^2/4 and x = π^2

A: Given function

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: Find the indicated midpoint rule approximation to the following integral. 2 元 4 sin x dx using n = 6…

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Q: Approximate the integral to three decimal places using the indicated rule. 9 cos(x) r0.9 dx;…

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Q: Evaluate the integral. (Use C for the constant of integration.) 3 cos x dx 6 + sin x

A: Evaluate the integral.

Q: How many times do you need to integrate by parts to reduce ff(In x)° dx to an integral of In x? ·

A: Given integral is ∫1eln x6dx

Q: Find the integral for the following functions: - dx 1) . Vx²-2x+1 2) ſ e3se c(x), sec(x). tan(x) dx…

A: Solution: The objective is to find the value of given integral

Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: 2 S sin (ax)cos(ax)dx

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Q: By finding an antiderivative, evaluate the integral, where the contour is any path between the…

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Q: The numerical value of the improper integral | (tx) 3 -dx is equal to .... (x++1) 2 00

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Q: Find the area under the curve y = sin 2t from t = 0 to t = π/4.

A: We have to find the area under the curve of a function y=sin2t , here we have the limit from 0 to…

Q: b. Find by double integration the area enclosed by the curve r= a(1+ cos 0) between 0 = 0 and 0=T.…

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Q: Evaluate the iterated integral. 4 (x + 3)dy dx Exact number, no tolerance. 4 (x + 3)dy dx = i

A: Let's find.

Q: Evaluate the integral. (Use C for the constant of integration.) cos(x) (4 + 8 sin²(x)) dx

A: Solve the intregal

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

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Q: find the indefinity integral  x^9 dx

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Q: Approximate the integral e-x dx as indicated below. Give your answer to 8 decimal places. Using the…

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