# Additional Techniques of Integration & Improper Integrals Calculus Questions

Question Description

I’m working on a calculus question and need support to help me understand better.

area: antiderivatives, areas and distances, the definite integral, evaluating integrals, FTC, integration by substitution, integration by parts, additional techniques of integration, improper integrals, areas between curves, volumes of solids, average value of a function, differential equations, direction fields, separable differential equations, exponential growth and decay, the logistic equation

Determine whether the integral converges or diverges and evaluate it if it converges:
ſi
1
√x 2 2
dx
J 2
Find g'(x) if
cost
g(x) =
dt
Jn 1+ t2
Find the solution of the differential equation that satisfies:
dy
xy’e”, y(0) =
1
dx
/* cosa o sinº o d
pur
DI
m!
10 wild boars are released inside a forest. Their population grows at a rate proportional to its
size. After 2 years, the population increases to 1000 (one thousand) boars.
(a) (5 pts) Find a formula for the boar population after t years.
(b) (5 pts) After how many years will the population reach 10000 (ten thousand) boars? You may
express your answer in terms of a logarithm.
10 wild boars are released inside a forest. Their population grows at a rate proportional to its
size. After 2 years, the population increases to 1000 (one thousand) boars.
(a) (5 pts) Find a formula for the boar population after t years.
(b) (5 pts) After how many years will the population reach 10000 (ten thousand) boars? You may
express your answer in terms of a logarithm.

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