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High School
Calculus and Analysis
Calculus 2
Applications of integrals

Recent questions in Applications of integrals

Yahir Crane 2022-06-10

What is the best description of exponential decay?

Oakey1w 2022-06-09

I'm having some trouble figuring out the right substitutions to make to integrate
$\int \sin^{4} (θ) d θ$
and
$\int \cos^{4} (θ) d θ$
Any hints or suggestions are welcome.

flightwingsd2 2022-06-09

Proving that this integral is divergent
$\int_{0}^{\infty} \frac{| \sin x |}{x^{2}}$

Gybrisysmemiau7 2022-06-09

What is the arc length of $f (x) = x - x e^{x}$ on $x \in [2, 4]$ ?

Villaretq0 2022-06-09

Integrating $\frac{x^{3}}{(81 - x^{2})^{2}}$

boloman0z 2022-06-08

What is the volume of the solid produced by revolving $f (x) = x^{2}, x \in [0, 4]$ around the x-axis?

manierato5h 2022-06-08

Integral with simple fractions: $\int_{} \frac{\cos x}{\sin x \sqrt{1 + \cos^{2} x}} d x$

Fletcher Hays 2022-06-08

Indefinite integral $\int \frac{\cos 2 x}{\sin^{4} x + \cos^{4} x} d x$

Eden Solomon 2022-06-08

What is the average value of the function $u (x) = 10 x \sin (x^{2})$ on the interval $[0, \sqrt{π}]$ ?

polivijuye 2022-06-08

How do you find the volume of the solid bounded by $x = y^{2}$ and the line x=4 rotated about the x axis?

Peyton Velez 2022-06-07

How to solve: $\int \frac{e^{x}}{e^{2 x} + 3} d x$
I tried substituting $u = e^{x}$ , $d u = e^{x} d x$ , and so I end up with:
$\int \frac{1}{u^{2} + 3} d u$
This looks like the derivative $\arctan (x)$ , but I have a 3 instead of a 1. How can I solve this integral?

Devin Anderson 2022-06-07

What is the surface area of the solid created by revolving $f (x) = \frac{1}{x^{2}}$ for $x \in [1, 2]$ around the x-axis?

Leland Morrow 2022-06-07

What is the surface area produced by rotating $f (x) = \frac{\sin x}{\cos x}, x \in [0, \frac{π}{4}]$ around the x-axis?

boloman0z 2022-06-06

How do you find the differential dy of the function $y = \frac{x + 1}{2 x - 1}$ ?

Finley Mckinney 2022-06-05

What is the arclength of $f (x) = \frac{1}{\sqrt{(x + 1) (2 x - 2)}}$ on $x \in [3, 4]$ ?

bulbareeh5kl 2022-06-04

How do you find the average value of the function for $f (x) = 1 + x^{2}, - 2 \leq x \leq 2$ ?

Kane Barr 2022-06-04

How do you use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and $y = x^{2}$ about the y-axis?

stud4kuj5bwn 2022-06-03

How do you find the average value of the function for $f (x) = \sqrt[3]{x}, 0 \leq x \leq 8$ ?

Kubjatkocn2cl 2022-06-03

How do you find the differential dy of the function $y = \sqrt{9 - x^{2}}$ ?

Matteo Brady 2022-06-02

What is the arc length of $f (x) = 6 x^{\frac{3}{2}} + 1$ on $x \in [5, 7]$ ?

There are numerous applications of integrals in Calculus 2. One of them that will help you understand this aspect is an application of Volterra integral equation. As you will learn, these must be divided into two groups where you have the first kind and then the second kind. You can take a look at the questions dealing with integrals that will also refer to Fredholm integral equation with the fixed constant. You should take a look at several answers and seek a detailed explanation that will explain the role of the unknown function as well.

Calculus 2

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