# Indefinite Integration Questions and Answers

Math

Indefinite IntegrationThe 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).

Math

Indefinite IntegrationEvaluate 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.

Math

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

Math

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

Math

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

Math

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

Math

Indefinite IntegrationWhat 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.

Math

Indefinite IntegrationEvaluate 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

Math

Indefinite IntegrationA 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

Math

Indefinite IntegrationOne 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?

Math

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

Math

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