Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [definite-integrals]

Questions about the evaluation of specific definite integrals.

A definite integral is defined as the area under a function from $a$ to $b$. Definite integrals sometimes involve calculating the indefinite integral, which is a function giving the area from $0$ to any $x$. However, definite integrals are most often separate from indefinite integrals in that the indefinite integral may not exist on its own. This is usually in the case of piece wise functions that are split along certain key points or integrals involving asymptotes.

20559 questions
0
votes
3 answers

value of $\int^{\infty}_{0}\sin(t)dt$

Finding value of $\displaystyle \int^{\infty}_{0}\sin(t)dt$ What i have tried yet As we know that period of $\sin(x)$ is $2\pi$ So we can split the intehral as $\displaystyle \lim_{n\rightarrow…
jacky
  • 5,194
0
votes
0 answers

Type of Integral question and source

in the question number 13 is an integration question, i am curious to know if there is a similar kind of questions like that that doesn't state the equation but only uses f(x), do you guys know what to search on the internet to find similar…
Godlixe
  • 333
0
votes
1 answer

Need help with a double integral

$$ \int_0^{1} \int_0^{\sqrt{1+x^2}} \frac{1}{\sqrt{x^2 + y^2}}\, dy dx $$ The question need to be solved using double integrals concept. I think the curve is rectangular hyperbola.
user766319
  • 1
0
votes
1 answer

Solving definite integral with module

The Integral given: $$\int_{z+2}^{z+4}e^{-{|x|}}dx$$ The problem is that if we divide the integral on two parts where $(|x|\ge0$ and $|x|<0)$ we will get this equation: $$\int_{z+2}^0e^x dx+\int_0^{z+4}e^{-x}dx = 2-e^{z+2}-\frac{1}{e^{z+4}}$$ which…
Никита
  • 19
0
votes
0 answers

estimation of an error of definite integral $<10^{-3}$

Using $$\int_{0}^{1}{x^{x}}dx = \sum_{n = 1}^\infty{\frac{{(-1)^{n-1}}}{{n^{n}}}}.$$ Estimate the Integral with an error of magnitude $<10^{-3}$ What i try Put $n=1$.Then sum is $\displaystyle 1$ Put $n=2$. Then sum is $\displaystyle…
DXT
  • 11,241
0
votes
2 answers

Is it possible to solve analytically this integral?

For my research, I've been modelling some experimental results and I stumbled upon this integral: $$\int_{x_0}^{x_1}\frac{1}{x}\frac{1}{1+e^{ax-b}}dx$$ where $x_0$, $x_1$, $a$ and $b$ $\in\mathbb{R}^+$. I've been trying to solve it analytically for…
josepmercadal
  • 243
0
votes
1 answer

Definite integration of divergent series

I think there is some mistake in the steps shown below. My objection is while integrating the function $f(x)$ we cannot directly put $1$ although the series when integrated has been substituted by $1$ directly. Kindly help me…
Akash Gautama
  • 373
0
votes
1 answer

Evaluation of definite Integration with unknown parameter $\alpha$

Evaluation of $\displaystyle \int^{\infty}_{0}\frac{x}{(x+\alpha)(x^4+x^2+1)}dx~,~~\alpha>0$ Let \begin{align} I &=\int^{\infty}_{0}\frac{x}{(x+\alpha)(x^4+x^2+1)}dx…
DXT
  • 11,241
0
votes
0 answers

Why Option B) is incorrect?

Let $f\left(x\right)\le x^5$ be a continuous function for all x $\epsilon$ R then $f\left(x\right)$ is A) All answers are wrong B) The integral average of $f(x)$ is on $[0,1]$ is positive C) The integral average of $f(x)$ is on $[0,1]$ is…
Feemo Fellow
  • 9
0
votes
1 answer

Definite integral - how to integrate

How to evaluate the first integral with respect to $dx$. If I take $x = a sin\theta$ how will the limits change?
danny
  • 906
0
votes
1 answer

definite integration with limit approches to infinity

Finding $\displaystyle \lim_{a\rightarrow\infty}\int^{1}_{0}\frac{\arctan(ax)\cdot \ln(1+x)}{1+x^2}dx$ What I try put $x=\tan \theta\,$ and $\,dx=\sec^2\theta\, d\theta$ $$I=\lim_{a\rightarrow\infty}\int^{\frac{\pi}{4}}_{0}\arctan(a\cdot…
jacky
  • 5,194
0
votes
2 answers

Trigonometric definite Integration with infinite limit

$$\displaystyle \lim_{n\rightarrow \infty}\frac{\int^{\frac{\pi}{2}}_{0}(\sin x+\cos x)^{n+1}dx}{\int^{\frac{\pi}{2}}_{0}(\sin x+\cos x)^{n}dx}$$ what i try Let…
jacky
  • 5,194
0
votes
1 answer

Why can't I find the area bounded by two curves this way?

I am trying to find the are bounded by: $x^2+3x-1$ and $x^2+3 \lfloor(x)\rfloor-1$ I first noticed that The area bounded by the curve can be represented as: $\int_{1}^{2} 3x-3 dx + \int_{2}^{3} 3x-6 dx +...+ \int_{n_1}^{n} 3x+3-3n dx $ Then, we can…
Henry Cai
  • 633
0
votes
1 answer

Confronting integrals

I have a solved exercise that estimate the divergence of $$\int _0^1\frac{1}{\log\left(2-t\right)}dt$$ using $\frac{1}{\log\left(2-t\right)}\sim \frac{1}{1-t}$ for $t\to 1$. So then $$\int _0^1\frac{1}{1-t}dt=\lim _{x\to 1}\left(\int…
giancarletto
  • 43
0
votes
1 answer

Sphere moment of inertia using disk method

Need to solve the moment of inertia of a sphere definined as the integral $\int\left(r^2\right)dm$ it can be rewritten as $\int\left(f(x)^2\right)pdV$ where dm= pdV and p represents the mass density of a sphere and $f(x)= sqrt(R^2-x^2)$ . The…
qubitz
  • 129
1 2 3
…
76 77