Indefinite Integration Questions and Answers

The rate of growth of profit (in millions) from an invention is approximated by P'(x)=xe OA. P(x) = -5e 1 OB. P(x) = -- ze OC. P(x) = -5e OD. P(x)=-e -+² -x² 1² +0.044 - 44,000 + 44,000 -0.044 where x represents time in years. The total profit in year 2 that the invention is in operation is $35,000. Find the total profit function P(x).

Evaluate the following integral using trigonometric substitution. ∫√64-x² dx Be sure your written work includes your trigonometric substitution (for x, dx) and the conversion back to the original variable.

Evaluate the following integral. ∫x2 +40x-16/x3-16x dx

Suppose F(7) = 10, F(8) = − 1, and F'(x) = f(x). 6 ∫ f(x) dx= 6

Find the indefinite integral using the substitution x = 10 sin(θ). (Use C for the constant of integration.) ∫1/(100 - x²)3/2dx

Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by parts. Use C for the constant of integration.) ∫ xe4x dx

Find the indefinite integral. 18/1 + 81x² dx

Find the general indefinite integral. (Use C for the constant Integration.) ∫(x^5)^1/4 dx

Find the indefinite integral. (Use C for the constant of integration.) ∫eˣ√(1-e²ˣ) dx

Evaluate the indefinite integral ∫41cos²(17x)dx

What is the exact volume of a solid that is formed with a square base, aligned with the center of the solid on the x-axis and the edge of the base following the function f(x) = 1/3 x on the [0, 9]? Note: Round to the nearest hundredth.

Evaluate the integral using the fundamental theorem of calculus when appropriate (your answer should be exact. Make sure you use C if needed.): f(x) = ∫(4x^2 –3x+4+3x-¹-x-^2) da

A factory is discharging pollution into a lake at the rate of r(t) tons per year given below, where t is the number of years that the factory has been in operation. Find the total amount of pollution discharged during the first 9 years of operation. (Round your answer to two decimal places.) r(t) = t/ t2 + 1

One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $144,500 to invest would like to have an income of $19,890 per year from her investments. How much should she invest at each rate?

Find the general solution of the differential equation. (Use C for the constant of integration.) dy/dx = 9x² / √(7 + x³) y =

Find the indefinite integral and check the result by differentiation. ∫(7x² +1/(3x)² ) dx