### Finding Integrals

Q#1) Find 6/5 ∫ ( x^ - 5 ---- ) dlx (Check by differentiating) X^3 Q#2) x^6 e^x - 4x ∫ -------------------- dlx X^6 Q#3) Find all antiderivatives if dl A ------ =

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Q#1) Find 6/5 ∫ ( x^ - 5 ---- ) dlx (Check by differentiating) X^3 Q#2) x^6 e^x - 4x ∫ -------------------- dlx X^6 Q#3) Find all antiderivatives if dl A ------ =

Q#1) dA --- = -6t^9 - 6t^4 + 4 dt A= ? Q#2) The rate of growth of the population, N(t), of a newly incorporated city t years after incorporation is estimated to be dN --- 1200sqrt(t) + 400, 0 < t < 16 (less than or equal to) dt If the population was

Please explain the steps and solutions, thanks: Evaluate the integrals: (ln x)² a) ∫ ‾‾‾x‾‾‾ dx b) ∫ x²e^x³dx c) x³ ∫ ‾‾‾‾‾ dx 1 + x² keywords: in

Please explain the steps and solutions, thanks: Use the Fundamental Theorem of Calculus to calculate the integrals: ² 3x² a) ∫ ‾‾‾‾‾‾ dx º (1 +x³) e sin(ln x) b) ∫ ‾

Stokes Theorem. See attached file for full problem description. Use Stokes Theorem to evaluate....

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x x Let F(x)= ∫ f(t) dt and G(x)= ∫ f(t) dt and f(t) > 1 for all t ≥ 0. 0 5 Is G(9)>G(5)? Explain. Can G(10) = 3? Explain.

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pi Use the fact that ∫ u²du = pi³/3 to evaluate the definite integral. º pi a) ∫ (pi x + x²)dx º ²x b) show that 2pi ≤ ∫ √1 + 3

Evaluate the definite integral using a graph of the integrand over the interval of integration 4 a) ∫ √ 2du -³ ¹ b) ∫ w dw -²

Please evaluate the integrals assuming that f is the function show on the graph on the attached document. Please explain the steps and solutions. See attached file for full problem description.

Integration of Exponential Functions. See attached file for full problem description.

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#7,8 and 9 Please see attached file.

A 6.00 in radius cylindrical rod is 2 ft long. Use a differential to approximate how much nickel (in in^3) is needed to coat the entire rod with the thickness of .12 in. keywords: integrals, integration, integrate, integrated, integrating, double, triple, multiple

Evaluate the double integral integral from y=0 to y=3 of integral from x=0 tp 1-y of (x+y)dxdy int ( int (x+y), x=0..1-y), y=0..3)

The function K is defined as the following (attached). Please evaluate Ck and dk step by step.

There are three problems in one question. a) in polar coordinates, write equations for the line x=1 and the circle of radius 2 centered at the origin b) write an integral in polar coordinates representing the area of the region to the right of x=1 and inside the circle c) evaluate the integral

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Regions and Curves. See attached file for full problem description.

Prove that if f(x) is even on [-a, a] and integrable on [0, a] where a>0, then f(x) is integrable on [-a, a] and Int([-a, a], f(x)dx) = 2*Int([0, a], f(x)dx).

10. Stock Values. Integrated Potato Chips paid a $1 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 4 percent per year. 1. What is the expected dividend in each of the next 3 years? 2. If the discount rate for the stock is 12 percent, at what price will the stock sell? 3. What is the exp

1. V(t) = 32t^2-8t, find position of particle on x axis at t = a, when t = 0, x = -6 2. L(d) = 167.5(sin(2 pi/366)(d-80))+738, find the day with the longest daylight.

Let S be the conic surface z = 3 sqrt (x^2 + y^2), where z is greater than or equal to 0 and less than or equal to 3. Find (double integral over S) z dS.

Find the area of the region bounded by: (using integrals) a)F (x) = 6x- x^2 and g(x)= x^2 - 2x b) y = x^2 - 4x and y = x-4 keywords: integration, integrates, integrals, integrating, double, triple, multiple

The marginal revenue for a certain product is given by dR/dx = 25-2x. Find the change in revenue when sales increase from 7 to 10 units. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Find y = f (x) if a) dy/dx = xe^(〖-x〗^2 ) and f(0) = 2 b) f"(x) = 1/e^x + 2 , f'(0) =3, f (0) = 1 keywords: integration, integrates, integrals, integrating, double, triple, multiple

Evaluate: a) ∫(〖 (2/x) + 3)〗^2 dx (using log) B) ∫_(-1)^2▒〖(2x-1)〗 dx C) ∫_0^1▒〖x√(1-x^2 )〗 dx Please show all work/steps.

Evaluate the double integral: / / l l (3x -2y)dA; R is the region enclosed by the circle l l x^(2) + y^(2) = 1 . / /

Suppose m is a positive measure on X, m(X) < inf f is an element of L^(inf), ||f||_inf<inf and a_n= int (|f|^n)dm for n = 1,2,... where the integral is evaluated over the set X Show that lim as n->inf of (a_(n+1))/(a_n) is equal to ||f||_inf