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Integrals

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 ------ =

Rates of Growth and Integration

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

Evaluate the Integrals

Please explain the steps and solutions, thanks: Evaluate the integrals: (ln x)² a) &#8747; &#8254;&#8254;&#8254;x&#8254;&#8254;&#8254; dx b) &#8747; x²e^x³dx c) x³ &#8747; &#8254;&#8254;&#8254;&#8254;&#8254; dx 1 + x² keywords: in

Stokes Theorem

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

Evaluating Definite Integrals

pi Use the fact that &#8747; u²du = pi³/3 to evaluate the definite integral. º pi a) &#8747; (pi x + x²)dx º ²x b) show that 2pi &#8804; &#8747; &#8730;1 + 3

Integration

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

Integrals : Volume of a Hollow Cylinder

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

Double Integral

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)

Polar Coordinates : Circles and Integrals

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

Finance/Accounting Problems

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

Conic Surfaces and Surface Integrals

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.

Areas of Bounded Regions

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

Change in revenue using integrals.

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

Integrals

Find y = f (x) if a) dy/dx = xe^(&#12310;-x&#12311;^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

Calculus III

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

Lp spaces

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